To estimate the variance of fill at a cannery, 10 cans were selected at random and their contents are weighed. The following data were obtained ( in ounces): 7.96, 7.90, 7.98, 8.01, 7.97, 7.96, 8.03, 8.02, 8.04, 8.02. Construct a 90% confidence interval for estimating the variance assuming that contents are normally distributed

Answers

Answer 1

We can state with 90% certainty that the cannery's actual fill variance lies between 0.001 and 0.005.

What is the confidence interval?

Using the chi-square distribution;

Given the data:

n = 10 (number of cans)

Sample weights: 7.96, 7.90, 7.98, 8.01, 7.97, 7.96, 8.03, 8.02, 8.04, 8.02

Sample mean (x):

x = (7.96 + 7.90 + 7.98 + 8.01 + 7.97 + 7.96 + 8.03 + 8.02 + 8.04 + 8.02) / 10 = 7.987

Sample variance (s²):

s² = [(7.96 - 7.987)² + (7.90 - 7.987)² + ... + (8.02 - 7.987)²] / (n - 1)

s² = 0.0015

Chi-square critical values:

The chi-square critical values are:

χ²_lower = 3.325

χ²_upper = 19.023

Confidence interval:

The confidence interval for estimating the variance is given by:

[(n - 1) * s² / χ²_upper, (n - 1) * s² / χ²_lower]

Confidence interval = [(10 - 1) * 0.0015 / 19.023, (10 - 1) * 0.0015 / 3.325]

= [0.000748, 0.004949]

The 90% confidence interval for estimating the variance is [0.001, 0.005].

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Related Questions

Please help, I’m sorry if it’s too much

Please help, Im sorry if its too much

Answers

Answer:

7)  x=u/10

8) a = - u/12

9) a = U/3 - 2/3

10) z = 0

11) a= n- p + m

12) x = gc/ y

13) a= w/k + v/k

14)x= pn/ m

Step-by-step explanation:

there... hope this helps!! also can i get brainliest? plz and thank you!!

at a sale this week, a table is being sold for $629. this is a 20% discount from the original price. what is the original price?

Answers

The original price of the table is $786.3

How to calculate the original price of the table ?

A table is being sold for $626

This price is a 20 percent discount from the original price

Therefore the original price can be calculated as follows

let x represent the original price of the table

629 = p(1-20/100)

629= p(1-0.2)
629= 0.8x

x= 629/0.8

x= 786.3

Hence the original price is $786.3

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1. Calculate p-tilde, the initial estimate for the proportion of cars with mpg of 100 or more.
a. 7/25=0.28
b. (7+2)/(25+4)=.310
c. (7+1)/(25+2)=.296

Answers

The correct option for p-tilde calculation is option c. (7+1)/(25+2)=.296.

The calculation of p-tilde, the initial estimate for the proportion of cars with mpg of 100 or more, is as follows:

We are given three options for the calculation of p-tilde as:

a. 7/25=0.28

b. (7+2)/(25+4)=.310

c. (7+1)/(25+2)=.296

We are supposed to choose the correct one among these.

Let's consider each option one by one:

a. 7/25=0.28

This option is calculating the proportion of cars with mpg of 100 or more by dividing the number of cars with mpg of 100 or more (which is 7) by the total number of cars (which is 25). So, the proportion is:

7/25=0.28

This is one of the options for p-tilde calculation.

b. (7+2)/(25+4)=.310

This option is calculating the proportion of cars with mpg of 100 or more by adding a prior count of 2 cars with mpg of 100 or more and 4 cars without it. So, the prior proportion is:

2/6 = 0.33

Now, the proportion of cars with mpg of 100 or more is calculated by adding the number of cars with mpg of 100 or more (which is 7) and the prior count (which is 2) and dividing by the total number of cars and the prior count (which is 25+4=29). So, the proportion is:

(7+2)/(25+4)=.310

This is the second option for p-tilde calculation.

c. (7+1)/(25+2)=.296

This option is calculating the proportion of cars with mpg of 100 or more by adding a prior count of 1 car with mpg of 100 or more and 2 cars without it. So, the prior proportion is:

1/3 = 0.33

Now, the proportion of cars with mpg of 100 or more is calculated by adding the number of cars with mpg of 100 or more (which is 7) and the prior count (which is 1) and dividing by the total number of cars and the prior count (which is 25+2=27). So, the proportion is:

(7+1)/(25+2)=.296

This is the third option for p-tilde calculation.

Therefore, the correct option for p-tilde calculation is option c. (7+1)/(25+2)=.296.

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Sharon asks Alana to describe her goals and current spending habits. Does Alana respond in the following way?

Answers

Answer:

Step-by-step explanation:

Which ways?

a large weather balloon is being inflated at a rate of 23 per minute. at what rate, in per minute, is the radius of the balloon changing when its radius is 5?

Answers

The rate at which the radius of the balloon is changing when its radius is 5 is approximately 0.0729 per minute.

To solve this problem, we can use the chain rule from calculus. Let's denote the radius of the balloon as r and the time as t.

Given:

- The balloon is being inflated at a rate of 23 per minute, which means the change in volume with respect to time is dV/dt = 23.

- We want to find the rate at which the radius is changing, which is dr/dt.

We know that the volume of a sphere is given by V = (4/3)πr³. To find the rate at which the radius is changing, we need to relate the rate of change of volume to the rate of change of the radius.

Differentiating both sides of the volume equation with respect to time (t), we get:

dV/dt = d/dt [(4/3)πr³]

To differentiate the right side of the equation, we can apply the chain rule:

dV/dt = (4/3)π * d/dt (r³)

Using the power rule for differentiation, we get:

dV/dt = (4/3)π * 3r²* dr/dt

Simplifying further, we have:

23 = 4πr² * dr/dt

Now we can solve for dr/dt:

dr/dt = 23 / (4πr²)

Substituting the given radius r = 5, we can calculate the rate at which the radius is changing:

dr/dt = 23 / (4π * 5²)

      = 23 / (4π * 25)

      = 23 / (100π)

      ≈ 0.0729 per minute

Therefore, when the radius of the balloon is 5, the rate of change of the radius is approximately 0.0729 per minute.

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Steve and his friends measured a snow pile; it was 7 feet tall. The next day, the
snow pile was only 6.5 feet tall. What was the percent of decrease in the snow
pile? Round your answer to the nearest tenth

Answers

The percentage decrease is 7.14%

First measurement = 7 feet

Second measurement = 6.5 feet

Difference in measurement = 7 feet - 6.5 feet = 0.5 feet

Percentage decrease = Difference in measurement/ First measurement × 100

= (0.5/7.0) × 100

= 7.14%

The percentage decrease is 7.14%

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The product of two consecutive positive integers is 17 more than 5 times their sum. Find the numbers​

Answers

Answer:

The no. are 11 and 12

Step-by-step explanation:

n(n+1)=17+5(2n+1)

n^2 +n=17+10n+5

n^2 -9n-22

Splitting the middle term

n^2 -11n+2n -22

n(n-11)+2(n-11)

(n-11)(n+2)

As n cannot ne negative,

n=11 and 12(consecutive no.)

Mark me brainliest!!

The two of the consecutive positive integers whose product is 17 more than 5 times their sum are 11 and 12.

What are Integers?

An integer is a complete number, therefore, not including the decimals and fractions. And it that can be either positive, negative, or zero.

Integer examples include -5, 1, 5, 8, 97, and 3,043.

Non-integer numbers include: -1.43, 1 3/4, 3.14, and more.

Let the first of the two consecutive integers be represented by x. Then, the other number can be written as (x+1).

Now, the product and the sum of the two numbers can be written as,

Product = x(x+1) = x² + x

Sum = x + (x+1) = 2x + 1

Further, it is given that the product of two consecutive positive integers is 17 more than 5 times their sum. Therefore, we can write,

x² + x = 17 + 5(2x + 1)

x² + x = 17 + 10x + 5

x² + x - 17 - 10x - 5 = 0

x² - 9x - 22 = 0

x² - 11x + 2x - 22 = 0

x(x - 11) + 2(x - 11) = 0

(x - 11)(x + 2) = 0

x = -2, 11

Thus, there are two numbers that can fulfil the given condition but since it is mentioned that we only need two positive consecutive integers. Therefore, the two numbers are 11 and 12.

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find the least common denominator of the rational expressions?

Answers

The least common denominator (LCD) of the rational expressions is (x+1)(x-1).

When adding or subtracting rational expressions, we need to find a common denominator. The least common denominator (LCD) is the smallest multiple of the denominators of the rational expressions.

To find the LCD, we follow these steps:

Factor the denominators of the rational expressions.Identify the common factors.Take the product of the highest powers of each common factor.If there are any unique factors, include them as well.Simplify the resulting expression to obtain the LCD.

Let's consider an example to illustrate this process:

Example:

Find the LCD of the rational expressions:

x/(x+1) and 1/(x-1)

Step 1: Factor the denominators:

x+1 and x-1

Step 2: Identify the common factors:

There are no common factors in this case.

Step 3: Take the product of the highest powers of each common factor:

Since there are no common factors, we skip this step.

Step 4: Include any unique factors:

The unique factors are x+1 and x-1.

Step 5: Simplify the resulting expression:

The LCD is (x+1)(x-1).

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The least common denominator of the rational expressions in this problem is given as follows:

4x(x + 5).

How to obtain the least common denominator?

The rational expressions for this problem are defined as follows:

9/(4x + 20), 10/(x² + 5x).

The denominators are given as follows:

4x + 20.x² + 5x.

The denominators can be simplified as follows:

4x + 20 = 4(x + 5).x² + 5x = x(x + 5).

The least common denominator is the multiplication of the unique factors, hence it is given as follows:

4x(x + 5).

Missing Information

The expression that completes this problem is given as follows:

9/(4x + 20), 10/(x² + 5x).

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Help!!! ASAP!! :3 Will Givve BRAINLIEST!!

Help!!! ASAP!! :3 Will Givve BRAINLIEST!!

Answers

Answer:

V = 672 cm³ (Option 3)

Step-by-step explanation:

Volume of Rectangular Prism = \(Length * Width * Height\)

Where L = 14 cm, W = 6 cm and H = 8 cm

V = 14 * 6 * 8

V = 672 cm³

What is 22 (Square root) rounded to the nearest whole number?

Answers

Answer:

\(\sqrt{22}\approx5\)

Step-by-step explanation:

We know that \(\sqrt{16}=4\) and \(\sqrt{25}=5\), so since 22 is closest to 25, then we can say that \(\sqrt{22}\approx5\)

Suppose Clare labels the books at a constant speed of s books per minute. Write an equation that represents the relatinoship between her labeling speed and the number of minutes it would take her to finish labeling. ​

Answers

it will take her 34 mins coz I said so innit

in a data ,range is 17 and coefficient of range is 0.2 find the smallest term of the data.
I will make brainelist to the best answer ​

Answers

Answer:

Step-by-step explanation:

Let largest value of data be L

and smallest value of data be S.

We are given that the range and coefficient of range of the data are 17 and 0.2 respectively.

Range formula is given by = Largest value - Smallest value

                   17  =   L - S

                  L = 17 + S ---------- [Equation 1]

Coefficient of range formula = (Largest - Smallest) ÷ (Largest + Smallest)

                                       0.2   =    l-s/l+s

                                      0.2 = 17/l+s

                 L + S = 17/0.2 = 85

So,    L + S = 85

       17 + S + S = 85   {using equation 1}

           2*S = 80

             S = 80/2 = 40

Putting value of S in equation 1, we get L = 20 + 40 = 60

Therefore,  Largest value, L = 60

               smallest value, S = 40

                         

vhhg

Step-by-step explanation:

rrgggggggjjhjjhgghghhh

Use the principle of mathematical induction to show that the statement is true for all natural numbers. Let P, denote the statement that (8 points) 5+9+13+17+. +(4n+1)=n(2n+3) Step 1. Verify the statement P is true (for n=1). Step 2. Write the statement P, (for n=k). Assume the statement P, is true. Step 3. Write the statement P₁., (for n=k+1) Use algebra to change the statement in Step 2 to the statement in Step 3. Step 4. Write a conclusion. (6 points) 10. Compute the first five terms in each sequence F=1, F₂=1, F=F₁+F

Answers

The first five terms in the sequence: 1, 1, 2, 3, 5 (Fibonacci sequence) The sequence F=1, F₂=1, F=F₁+F will look like 1,1+1=2,1+2=3, 2+3=5,3+5=8. P₁ is true.

Statement P is given as 5+9+13+17+. . . +(4n+1)=n(2n+3)Step 1:For n=1,5+9=14 and 1(2(1)+3)=5Hence, P is true for n=1.Step 2:Suppose, for n=k, P is true. So, 5+9+13+…+(4k+1)=k(2k+3) We need to show P is true for n=k+1.Step 3:When n=k+1,5+9+13+…+(4k+1)+(4(k+1)+1)=(k+1)(2(k+1)+3)RHS= (k+1)(2k+5)k(2k+3)+8(k+1)=5k+3+8k+8=13k+11LHS= 5+9+13+…+(4k+1)+(4(k+1)+1)=k(2k+3)+(4(k+1)+1)=2k²+7k+5=13k+11

Therefore, P₁ is true. Step 4:By the principle of mathematical induction, the statement P is true for all natural numbers.10.

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Please help asap thank you!!!

Please help asap thank you!!!

Answers

Answer: (3,-5) minimum

Step-by-step explanation:

the vertex is at the bottom so it is a minimum

O points

A 18 inch pizza is cut into 8 slices. What is the area of each slice?(sector

area)

Answers

Answer:

1/2

Step-by-step explanation:

ANSWER CORRECTLY FOR BRAINLIEST!!!

ONLY:

8.

9.

10.

11.

ANSWER CORRECTLY FOR BRAINLIEST!!!ONLY:8.9.10.11.

Answers

Answer:

8. -1

6-9=-3

-3/3=-1

8/ 9 + 3X = 6 => X = -1
The number is -1

9/ 9(x-1) - 4(7-x) <= 10x - (2x + 1) - 6
=> 9x - 9 - 28 + 4x <= 10x - 2x - 1 - 6
=> 13x - 37 <= 8x - 7
=> 5x <= 30
=> x <= 30/5
=> x <= 6

A random sample of 169 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.8 ounces. In this problem, what is the 0.8?
a)a statistic
b)the standard error of the mean
c)a parameter
d)the average content of colognes in the long run

Answers

The value 0.8 is the standard deviation of the contents and it represents a parameter in this context.

In statistics, a parameter refers to a characteristic or measure of a population, while a statistic refers to a characteristic or measure calculated from a sample. In this problem, the standard deviation of 0.8 ounces represents a parameter because it is given as the standard deviation of the population of cologne bottle contents. Parameters are typically unknown and are estimated using statistics, which are calculated from sample data.

In contrast, the standard error of the mean is a measure of the variability of the sample mean and is calculated as the standard deviation of the sample divided by the square root of the sample size. It is used to estimate the variability of the sample mean from different samples.

Therefore, in this problem, the value 0.8 represents the standard deviation of the population and is considered a parameter.

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Let the random variable X and Y have joint p.d.f
f(x,y)=47(x2+3y2),0 (a) Find the marginal densities of X and Y.
(b) Find the c.d.f of X and c.d.f of Y.
(c) Determine the conditional p.d.f's.
(d) Find E(X) and E(Y).
(e) Find Var(X) and Var(Y).
(f) Find Cov(X,Y).

Answers

According to the cost function,

(a) The marginal densities of X and Y are 47.333x² and 47.333y² respectively.

(b) The c.d.f of X is 15.777x³ and c.d.f of Y is 15.777y³

(c) The conditional p.d.f's is (x² + 3y²)/x²

(d) The values of E(X) isand E(Y) is

(e) The values of Var(X) is and Var(Y) is

(f) The value of Cov(X,Y) is 0.

To answer the questions posed in this problem, we need to use the joint p.d.f to find various properties of X and Y. We will start by finding the marginal densities of X and Y. The marginal density of X is the probability distribution of X alone, and similarly for Y. To find the marginal density of X, we need to integrate the joint p.d.f over all possible values of Y:

f(x)(x) = ∫ f(x,y) dy

= ∫ 47(x² + 3y²) dy, from 0 to infinity

= 47x²∫(1+3(y/x)²)dy, from 0 to infinity

= 47x²(1+0.333...)

= 47.333x²

Similarly, the marginal density of Y can be found by integrating the joint p.d.f over all possible values of X:

f(y)(y) = ∫ f(x,y) dx

= ∫ 47(x² + 3y²) dx, from 0 to infinity

= 47y²∫(1+(x/(√3y))²)dx, from 0 to infinity

= 47.333y²

Next, we need to find the cumulative distribution functions (c.d.f) of X and Y. The c.d.f of a random variable gives the probability that the variable takes on a value less than or equal to a specified value. The c.d.f of X is:

f(x)(x) = P(X ≤ x) = ∫ f(x)(u) du, from 0 to x

= ∫ 47.333u² du, from 0 to x

= 15.777x³

Similarly, the c.d.f of Y is:

f(y)(y) = P(Y ≤ y) = ∫ f(y)(v) dv, from 0 to y

= ∫ 47.333v² dv, from 0 to y

= 15.777y³

Now we can find the conditional probability density functions (p.d.f) of X and Y given the other variable. The conditional p.d.f of X given Y is:

f(x)|Y(x|y) = f(x,y)/f(y)(y)

= 47(x² + 3y²)/47.333y²

= (x² + 3y²)/y²

Similarly, the conditional p.d.f of Y given X is:

f(y)|X(y|x) = f(x,y)/f(x)(x)

= 47(x² + 3y²)/47.333x²

= (x² + 3y²)/x²

Using these conditional p.d.f's, we can find the expected values (means) of X and Y:

E(X) = ∫ xf(x)(x) dx, from 0 to infinity

= ∫ 47.333x³ dx, from 0 to infinity

= ∞

This means that the expected value of X does not exist. Similarly, we can show that E(Y) also does not exist.

To find the variances of X and Y, we need to use the definitions of variance, which is the expected value of the squared deviation from the mean. However, we can use an alternate definition of variance in terms of the second moments:

Var(X) = E(X²) - [E(X)]²

= ∫ x²f(x)(x) dx - [∞]²

= ∫ 47.333x^4 dx - [∞]²

= ∞

Similarly, we can show that Var(Y) also does not exist.

Finally, we need to find the covariance between X and Y, which measures the degree of linear dependence between the two variables. The covariance is defined as:

Cov(X,Y) = E[(X - E(X))(Y - E(Y))]

= ∫∫ (x - E(X))(y - E(Y))f(x,y) dx dy

= ∫∫ xyf(x,y) dx dy - E(X)E(Y)

= ∫∫ 47(x³y + 3y³x) dx dy - ∞ x ∞

= 0

Here, we have used the fact that E(X) and E(Y) do not exist. Therefore, the covariance between X and Y is zero, indicating that the two variables are uncorrelated.

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The tangent of angle B is __

The tangent of angle B is __

Answers

Answer:

\(\frac{\sqrt{95} }{7}\)

Step-by-step explanation:

The tangent is equal to the opposite/adjacent

the opposite of angle b is √95 and the adjacent of angle b is 7 so the tangent of angle b is \(\frac{\sqrt{95} }{7}\)

3x-2 is less than or equal to -20

Answers

Answer:

x \(\leq\) -6

Step-by-step explanation:

3x - 2 \(\leq\) -20

Solve for x:

3x \(\leq\) -18

x \(\leq\) -6

The answer is -6 which means it is less than

3) A lottery ticket says that the chances of winning are 1 in 8. Suppose you buy 10 of these lottery tickets. Find the probability that at least one of them will be a winner

Answers

The probability of at least one of your 10 lottery tickets being a winner is approximately 0.638 or 63.8%.

The probability of winning on a single lottery ticket is 1/8, which means that the probability of not winning is 7/8. If you buy 10 of these lottery tickets, the probability of not winning on any of them is:

(7/8)^10 = 0.362

This means that there is a 36.2% chance that none of your tickets will be a winner. To find the probability that at least one of your tickets will be a winner, we can use the complementary probability:

P(at least one winner) = 1 - P(no winners)

P(at least one winner) = 1 - 0.362

P(at least one winner) = 0.638

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Find the lowest common multiple of 36
and 72

Answers

36x2 =72 so that’s your answer

PLEASE ANSWER ASAP!! Georgia is a farmer and wants to plant a crop of tomato plants so she can sell her crop at the local farmer's market. She already has a large number of plants cultivated from last year's harvest. Each should produce an average of 35 tomatoes per plant during the growing season. She has found a nursery to buy more tomato plants at which are a different type. She found that these tomato plants will cost $5.25 each and should produce 25 tomatoes per plant on average over the course of the growing season. When planting, she wants to arrange the plants so that there are 5 fewer plants in each column than there are in each row. Georgia can spend no more than $500 on the tomato plants. In order to meet customer demands, she needs to produce at least 5,000 tomatoes during the growing season. Let x represent the number of plants in a row, and let y represent the number of plants that Georgia already has. Create a system of inequalities to find the number of plants in a row and the number of plants Georgia already has, and use it to determine how many of the solutions are viable.

A. Part of the solution region includes a negative number of tomato plants in a row; therefore, not all solutions are viable for the given situation.

B. There is no solution region.

C. None of the solution region is viable because there cannot be a negative number of tomato plants in a row and she can not have a negative number of tomato plants already on hand.

D. The entire solution region is viable.

Answers

Answer is C! I got it off of someone else sorry if you want an explenation i dont have that for you :/

Answer:

Part of the solution region includes a negative number of tomato plants in a row; therefore, not all solutions are viable for the given situation.

Step-by-step explanation:

got right on edmentum/plato

write the hypotheses to test if the success rate for art at this clinic is significantly higher than the success rate reported by the cdc.

Answers

In contrast to the CDC's reported success rate, the success rate for art at this clinic is substantially greater.

what is null hypothesis ?

A claim or assumption that there is no statistically significant difference between two populations or sets of data is known as the null hypothesis. It serves as the beginning point for statistical hypothesis testing and is typically indicated as H0. According to the null hypothesis, any observed difference between the populations or data sets is the result of sampling error or random chance rather than a genuine difference.

given

The success rate for art at this clinic is not statistically different from the CDC's claimed success rate.

In contrast to the CDC's reported success rate, the success rate for art at this clinic is substantially greater.

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Write an equation in slope-intercept form for the graph shown.

Write an equation in slope-intercept form for the graph shown.

Answers

Answer:

y= 2x-3

Step-by-step explanation:

4/2 OR 2 is the slope

-3 is the intercept  




Given f(x) = 3x2 + kx – 7, and the remainder when f (x) is divided by x – 4 is
81, then what is the value of k?

Answers

Answer:

-243

Step-by-step explanation:

{3׳ykx-7 incluye

Given f(x) = 3x2 + kx 7, and the remainder when f (x) is divided by x 4 is81, then what is the value

What is a in 5a + 3 = 18?

Answers

Answer:

a = 3

Step-by-step explanation:

5a + 3 = 18

5a = 15

a = 3

Answer:

Hello

⤵️

Step-by-step explanation:

5a = 18-3 = 15

A = 15÷5

A= 3

hope it helps

Please help and explain

Please help and explain

Answers

Answer:

C

Step-by-step explanation:

I tend to remember the "U" symbol as meaning "or", whilst the "n" symbol means aNd.

using this method we can see that the question is asking us to find which diagram fills in a shade that is NOT x OR y.

Option A shades Y Option B shades X aNd Y (X n Y)Option D shades X

So therefore the answer must be C as it shades in all area that isn't X OR Y!

40% of Damien‘s marbles are blue. Damien has three marbles how many of the marbles are not blue

Answers

40% of Damien’s marbles are 6/5 or 1.2.

What is a percentage?

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Damien has three marbles.

40% of Damien’s marbles are blue.

That means,

40% of 3 blue marbles.

So, using the percentage formula,

40% of 3,

= 40 x 3/100

= 120/100

= 12/10

= 6/5

= 1.2

Therefore, 1.2 marbles are blue.

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three people are selected from a group of 8 freshmen and 6 sophomores. the probability 2 freshmen and 1 sophomore are selected is

Answers

Answer:  The probability that 2 freshmen and 1 sophomore are selected is 42/91.

Step-by-step explanation:

To obtain the probability that 2 freshmen and 1 sophomore are selected from a group of 8 freshmen and 6 sophomores, we can use the combinations formula:

The total number of ways to select 3 people from a group of 8 + 6 = 14 people is:  

C(14, 3) = 14! / (3! * 11!) = 364

The number of ways to select 2 freshmen from a group of 8 freshmen is: C(8, 2) = 8! / (2! * 6!) = 28

The number of ways to select 1 sophomore from a group of 6 sophomores is: C(6, 1) = 6! / (1! * 5!) = 6

Therefore, the number of ways to select 2 freshmen and 1 sophomore from the group of 14 people is: 28 * 6 = 168

The probability of selecting 2 freshmen and 1 sophomore is:P(2F, 1S) = 168 / 364 = 42 / 91

Therefore, the probability that 2 freshmen and 1 sophomore are selected is 42/91.

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