Which of the following statements are correct? A. The statement that the random variable X is normally distributed with parameters is often abbreviated . B. If the random variable X is normally distributed with parameters , then . C. The graph of any normal probability density function is symmetric about the mean and bell-shaped, so the center of the bell (point of symmetry) is both the mean of the distribution and the median. D. If the random variable X is normally distributed with parameters , then a large implies that a value of X far from may well be observed, whereas such a value is quite unlikely when is small. E. All of the above statements are correct

Answer:

34 5/8

Step-by-step explanation:

you just add all the numbers on the left and the two drawer numbers then boom!!

Answer:

a) Chi square value = 1.031

b) There is no significant difference between the observed and expected values.

c) Check explanations for the part C of the question

Step-by-step explanation:

a) People away from work due to lower back injuries:

Observed value = 18

Expected value = 14.3

People away from work due to other injuries:

Observed value = 200 - 18 = 182

Expected value = 185.7

The chi square value is calculated by the formula:

[tex]x^{2} = \frac{(O-E)^{2} }{E}[/tex]

For people out of work due to lower back injuries:

Chi square value,

[tex]x^{2} = \frac{(18-14.3)^{2} }{14.3} \\x^{2} = 0.957[/tex]

For people out of work due to other injuries:

Chi square value,

[tex]x^{2} = \frac{(182-185.7)^{2} }{185.7} \\x^{2} = 0.074[/tex]

Total chi square value for the distribution:

[tex]x^{2} = 0.074 + 0.957\\x^{2} = 1.031[/tex]

b) The degree of freedom, df = n -1

n = 2 ( two categories of people are considered)

df = 2-1 = 1

For df = 1 and, chi square = 1.031

P - value = 0.3099

p- value = 0.3099, the result is not significant at p < 0.05

There is no significant difference between the observed and expected values.

c) Hypothesis testing helps the safety professionals to statistically analyse any situations and determine whether or not they are safe. It can help them to predict the outcome of a given situation by making necessary observations.

Answer:

99.5% of all samples of 21 of​ today's women in their 20's have mean heights of at least 65.86 ​inches.

Step-by-step explanation:

We are given that a half-century ago, the mean height of women in a particular country in their 20's was 64.7 inches. Assume that the heights of​ today's women in their 20's are approximately normally distributed with a standard deviation of 2.07 inches.

Also, a samples of 21 of​ today's women in their 20's have been taken.

Let [tex]\bar X[/tex] = sample mean heights

The z-score probability distribution for sample mean is given by;

                          Z = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = population mean height of women = 64.7 inches

            [tex]\sigma[/tex] = standard deviation = 2.07 inches

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the sample of 21 of​ today's women in their 20's have mean heights of at least 65.86 ​inches is given by = P([tex]\bar X[/tex] [tex]\geq[/tex] 65.86 inches)

  P([tex]\bar X[/tex] [tex]\geq[/tex] 65.86 inches) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{65.86-64.7}{\frac{2.07}{\sqrt{21} } }[/tex] ) = P(Z [tex]\geq[/tex] -2.57) = P(Z [tex]\leq[/tex] 2.57)

                                                                        = 0.99492  or  99.5%

The above probability is calculated by looking at the value of x = 2.57 in the z table which has an area of 0.99492.

Therefore, 99.5% of all samples of 21 of​ today's women in their 20's have mean heights of at least 65.86 ​inches.

Answer:

(a) Find the probability of type I error. = 0.1018

Step-by-step explanation:

check attachment for the answer

Answer:

The probability of Type I error is = 0.10185.

Step-by-step explanation:

Solution:-

The type I - error is defined as the probability of rejecting Null hypothesis defined by Alternate hypothesis:

                          Ha : X ≥ 8

Where,

X : Denote the number of cars crash with no visible damage

The random variate "X" is defined by binomial distribution:

                            X ~ B ( n = 20 , p = 0.25 )

- The probability of Type I error:

                        P (Type I error ) = P ( Reject Null hypothesis )

                                                   = P ( X ≥ 8 )

- The probability mass function of binomial random variate "X" is given:

                     [tex]P ( X = x ) = nCr (p)^r * (1-p)^(^n^-^r^)\\P ( X \geq 8 ) = 1 - P ( X < 8 )\\\\P ( X \geq 8 ) = 1 - [ P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P ( X = 4 ) + P ( X = 5 ) + P ( X = 6 ) + P ( X = 7 ) ][/tex][tex]P ( X \geq 8 ) = 1 - [ (0.75)^2^0 + 20(0.25)*(0.75)^1^9 + 20C2(0.25)^2*(0.75)^1^8 +\\\\ 20C3(0.25)^3*(0.75)^1^7 + 20C4(0.25)^4*(0.75)^1^6 + 20C5(0.25)^5*(0.75)^1^5\\\\ + 20C6(0.25)^6*(0.75)^1^4 + 20C7(0.25)^7*(0.75)^1^3 ] \\\\\\P ( X \geq 8 ) = 1 - [ 0.00317 + 0.02114 + 0.06694 + 0.13389 + 0.18968 + 0.20233\\\\+ 0.16860 + 0.11240]\\\\P ( X \geq 8 ) = 1 - 0.89815 = 0.10185[/tex]

Answer: The probability of Type I error is = 0.10185.

Answer:

Speed = x/t = 146.61/2 = 73.30 mph

direction y = 22.59° northeast

Step-by-step explanation:

Given;

The distance from Parrot Point Airport to the Ivy Cliffs is 172 miles at and angle of 7.0 degrees northeast;

Resultant distance R = 172 (7° northeast)

Time given to make the trip t = 2 hours

Distance moved by wind during the time dw = 25×2 = 50 miles south east.

Let x represent the distance covered by plane without wind during the time and y the direction;

Resolving into horizontal and vertical component;

horizontal;

x cosy + 50cos45 = 172cos7

xcosy = 172cos7 - 50cos45 .....1

Vertical;

xsiny - 50sin45 = 172sin7

xsiny = 172sin7 + 50sin45 .....2

Divide equation 2 by 1

xsiny/xcosy = (172sin7 + 50sin45)/(172cos7 - 50cos45)

tany = 0.4160

y = taninverse (0.4160)

y = 22.59° northeast

Substituting y into equation 2;

xsin22.59 = 172sin7 + 50sin45

x = (172sin7 + 50sin45)/sin22.59

x = 146.61 miles

Speed = x/t = 146.61/2 = 73.30 miles per hour

Speed = 73.30mph

Answer:

Dependent sample: The same textbook are being compared.

Step-by-step explanation:

We are given the following in the question:

A student wants to compare textbook prices for two online bookstores.

Sample 1 from bookstore A:

$115, $43, $99, $80, $119

Sample 2 from bookstore B:

$110, $40, $99, $69, $109

Dependent and independent sample:

Thus, the given sample is dependent sample as the same textbook is being compared from two different bookstore.

The textbook prices listed for the two different online bookstores are dependent samples, as the prices are paired for the same textbooks across the two bookstores. Analyzing this data would involve using statistical methods suitable for dependent samples, like paired t-tests.

The textbook prices listed by the student for the two different online bookstores represent dependent samples. This is because the prices are paired for the same textbooks across the two bookstores. They are not independent samples because the price of a given book in one store could potentially influence the price of the same book in the other store. For example, if one store lowers its prices, the other might follow suit to remain competitive.

Consideration of such data requires the analysis method suitable for dependent samples. Specifically, using methodologies like paired t-tests in statistics might be appropriate in this scenario to compare the prices from the different online bookstores. These methods account for the fact that measurements within each pair could be correlated.

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Step-by-step explanation:

Let Xb be the no of braclets made

Let Xn be the no of necklaces made

Max Z=250Xb + 500Xn (Objective Function)

Subject to

2Xb + 5Xn <= 625 (rubies)

3Xb + 7 Xn <= 800 ( diamonds)

4Xb + 3 Xn <= 700 (Emeralds)

Xb>=0 (non-negativity)

Xn >= 0 (non negativity

Answer:

Step-by-step explanation:

We are to Formulate the question given as a Linear Programming problem with the objective of maximizing profit.

From the question;

Kings will sell each bracelet for $400 and it costs them $150 to make it.

This implies that; King will net a profit on $250 on each bracelet made with 2 rubies, 3 diamonds, and 4 emeralds :

Also;

Kings will sell each necklace for $700 and it costs them $200 to make it

i.e King will net a profit of $500 on each necklace  made with 5 rubies, 7 diamonds, and 3 emeralds.

Now; let's assume that :

[tex]Y_{br}[/tex]  be the no of bracelets made ;   &

[tex]Y_{nk}[/tex]  be the no of necklaces made

[tex]\\ \\Max \ Z=250 \ Y{_b_r}} + 500 \ Y{_n_k}[/tex]    (Objective Function)

Subject to :

[tex]2 \ Y_{br} + 5 \ Y_{nk}[/tex] ← 625 (rubies)

[tex]3 \ Y_{br} + 7 \ Y_{nk}[/tex] ← 800 ( diamonds)

[tex]4 \ Y_{br} + 3 \ Y_{nk}[/tex] ← 700 (Emeralds)

[tex]\\ \\Y_{br} \\[/tex] ⇒ 0 (non-negativity)

[tex]\\\\ \ Y_{nk}\\[/tex] ⇒ 0 (non negativity)

Answer:

Your answer is 1341.75

Step-by-step explanation:

3/4 x 1440 = 1080

1080 + 295.25 = 1375.25

1375.25 + -33.50 = 1341.75

The solution of the given expression 3/4(1440) + 295.25 + (-33.50) involving multiplication, addition, and subtraction in mathematics is equal to 1341.75.

The expression provided is:

3/4(1440) + 295.25 + (-33.50)

To solve this, we need to follow the order of operations (PEMDAS):

Multiply 3/4 by 1440 to get 1080.

Add 1080 to 295.25 to get 1375.25.

Finally, subtract 33.50 from 1375.25 to get the final answer of 1341.75.

The amount by which we must raise the price in order to retain your existing dollar profit margin is $2.04; the right solution is (a).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

There was a trucking strike that caused a prime ingredient in your menu item to shoot up by 17%. You were paying $12 per package.

The increases in the price of the ingredient = 17% of 12

Increase = 0.17 × 12            

Increase = 2.04

Therefore, the amount by which we must raise the price in order to retain your existing dollar profit margin is $2.04; the right solution is (a).

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The price of the menu item should be increased by $2.04.

Let's begin by calculating the new cost per package after the price increase. If the original cost per package was $12 and it increased by 17%, we calculate the increase as follows:

Increase = 12 * 0.17 = 2.04

The new cost per package will be:

New cost = 12 + 2.04 = 14.04

To maintain the same dollar profit margin on your menu item, you need to increase the price by the same amount as the cost increase, which is $2.04.

Answer:

I'd say go to Wikipedia and look it up.  It is something that cannot be summarized into just a few words.

Step-by-step explanation:

Answer:

The complete Python program to calculate the monthly payment on a loan with step by step explanation is given below.

Python Code with Explanation:

# get the loan amount from the user

LoanAmt=eval(input("Please enter the loan amount: "))

# get the annual interest rate from the user in percentage form

InterestRate=eval(input("Please enter the annual interest rate in percentage: "))

# get the number of months from the user

NumberMonths=eval(input("Please enter the number of months: "))

# convert the annual interest rate into monthly interest rate and also into decimal form according to the equation given in the question

MonthlyRate = InterestRate/1200

# implement the given equation to find out the required monthly payment, the operator (**) is used to raise to the power

Payment = (LoanAmt*MonthlyRate (1+MonthlyRate)**NumberMonths)/((1+MonthlyRate)**NumberMonths -1)

# finally, print the monthly payment

print("The monthly payment is: ", Payment)

Output:

Please enter the loan amount: 1500

Please enter the annual interest rate in percentage: 15

Please enter the number of months: 12

The monthly payment is: 135.38746851773584

Bonus:

You can use this command to limit the digits after the decimal point

For example following code will limit to 2 digits after the decimal point.

print(format(Payment, '.2f'))

Answer:

[tex]F(s) = \frac{s(e^{\pi s}+1)}{s^2 +1}[/tex]

Step-by-step explanation:

Using the formula for Laplace the transformations if [tex]F(s)[/tex]  is the converted function then

[tex]F(s) = \int\limits_{0}^{\infty} e^{-st} \cos(t) dt = \int\limits_{0}^{\pi} e^{-st} \cos(t) dt[/tex]

To solve that integral you need to use integration by parts, when you do integration by parts you get that

[tex]F(s) = \frac{s(e^{\pi s}+1)}{s^2 +1}[/tex].

Answer:

The laplace transform is [tex] F(s) = \frac{s(1+e^{-s\pi})}{s^2+1}[/tex]

Step-by-step explanation:

Let us asume that f(t) =0 for t<0. So, by definition, the laplace transform is given by:

[tex]I = \int_{0}^\pi e^{-st}\cos(t) dt[/tex]

To solve this integral, we will use integration by parts. Let u= cos(t)  and dv = [tex]e^{-st}[/tex], so v=[tex]\frac{-e^{st}}{s}[/tex] and du = -sin(t), then, in one step of the integration we have that

[tex]I = \left.\frac{-\cos(t) e^{-st}}{s}\right|_{0}^\pi- \int_{0}^\pi \frac{\sin(t) e^{-st}}{s} dt[/tex]

Let [tex] I_2 = \int_{0}^\pi \frac{\sin(t) e^{-st}}{s} dt[/tex]. We will integrate I_2 again by parts. Choose u = sin(t) and dv = [tex]\frac{e^{-st}}{s}[/tex]. So

[tex] I_2 = \left.\frac{-\sin(t) e^{-st}}{s^2}\right|_{0}^\pi + \int_{0}^\pi \frac{\cos(t) e^{-st}}{s^2}dt [/tex]

Therefore,

[tex]I = \left.\frac{-\cos(t) e^{-st}}{s}\right|_{0}^\pi - (\left.\frac{-\sin(t) e^{-st}}{s^2}\right|_{0}^\pi - \frac{1}{s^2} I[/tex]

which is an equation for the variabl I. Solving for I we have that

[tex]I(\frac{s^2+1}{s^2}) =\left.\frac{-\cos(t) e^{-st}}{s}\right|_{0}^\pi+\left.\frac{\sin(t) e^{-st}}{s^2}\right|_{0}^\pi[/tex]

Then,

[tex]I = \left.\frac{-s\cos(t) e^{-st}}{s^2+1}\right|_{0}^\pi+\left.\frac{\sin(t) e^{-st}}{s^2+1}\right|_{0}^\pi[/tex].

Note that since the sine function is 0 at 0 and pi, we must only care on the first term. Then

[tex]I = \left.\frac{-s\cos(t) e^{-st}}{s^2+1}\right|_{0}^\pi = \frac{s}{s^2+1}(1-(-1)e^{-s\pi}} = \frac{s(1+e^{-s\pi})}{s^2+1}[/tex]

Answer:

a) [tex]f(401) = 3010[/tex], b) [tex]f(400.5) = 3005[/tex], c) [tex]f(399) = 2990[/tex], d) [tex]f(398) = 2980[/tex], e) [tex]f(399.75) = 2997.5[/tex]

Step-by-step explanation:

The estimation of each value can be found by the following value:

[tex]f(x + \Delta x) = f(x) + f'(x)\cdot \Delta x[/tex]

a) [tex]f(401) = 3000 + 10\cdot (401-400)[/tex]

[tex]f(401) = 3010[/tex]

b) [tex]f(400.5) = 3000 + 10\cdot (400.5 - 400)[/tex]

[tex]f(400.5) = 3005[/tex]

c) [tex]f(399) = 3000 + 10\cdot (399 - 400)[/tex]

[tex]f(399) = 2990[/tex]

d) [tex]f(398) = 3000 + 10\cdot (398-400)[/tex]

[tex]f(398) = 2980[/tex]

e) [tex]f(399.75) = 3000 + 10\cdot (399.75-400)[/tex]

[tex]f(399.75) = 2997.5[/tex]

Answer:

2047.5 kg

Step-by-step explanation:

There's a total of 454545 kg of meat, and each dragon gets x kg. There are 222 dragons. So, we have the equation: 222x = 454545

Divide by 222 from both sides: x = 2047.5 kg

Thus, each dragon gets 2047.5 kg of meat.

Hope this helps!

Answer:

$226,300

Step-by-step explanation:

Given Allowance for Doubtful Accounts is estimated as $205,000 and Allowance for Doubtful Accounts has a debit balance of $21,300

#The  amount of the adjusting entry for uncollectible accounts is calculated as below:

[tex]Adjustment \ Cost=Allowance\ Doubtful\ Accounts +Doubtful \ Accounts \ Debit \ Balance\\\\=205000+21300\\\\\$226,300[/tex]

Hence,  the amount of the adjusting entry for uncollectible accounts is $226,300

Answer:

48-15 is 33

Step-by-step explanation:

Answer:

1/81

Step-by-step explanation:

P(1st ticket is a winner) = 1/9

These are independent events

P(2nd ticket is a winner) = 1/9

P (winner, winner) = 1/9 * 1/9 = 1/81

Answer: The inequality could be t > 900. Draw a number line so it includes 900. Draw an open circle on 900. Shade all the numbers greater than 900, or to the right.

Step-by-step explanation:

Inequality- Inequality is the something that is equal to the something or less than that of the sign give the conditions on which the graph is drawn on the basis of sales occured profits occured

Explanation to the above is the that mentioned below:

Thus we conclude that from the above the graph of the equation is solid line.

To know about the Inequality

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The probability of getting a tail on the next coin flip remains at 50 percent, regardless of the previous series of outcomes because each coin flip is an independent event.

The question is concerned with the probability of getting a tail after having tossed a coin 100 times and obtaining 67 heads and 33 tails. Despite the past results of these tosses, the coin still has a 50 percent chance of landing on heads or tails on any given flip. This concept is based on the idea that each coin flip is an independent event with its own probability, unaffected by previous outcomes.

To answer the student's question directly, the probability that the next flip results in a tail is still 50 percent because past results do not change the probability of future coin flips. This is supported by the law of large numbers, which states that as the number of trials increases, the relative frequency of results will get closer to the expected probability.

There is no sample given, please provide us with an attachment for your answer.

Answer:

Please post another question with the angle that you were given. Thank you!

Step-by-step explanation:

There wasn't any angles given therefore, I couldn't help!

In a one-sample t-test, the normal distribution of sample means is more important than the normality of individual data in the population. This follows the Central Limit Theorem which states that, with a decently large sample size, the distribution of sample means will approach normality regardless of the population distribution.

Statement C is the correct option. The Central Limit Theorem indicates that regardless of the population distribution, as long as we have a sufficiently large sample size, the sample means will be approximately normally distributed. However, this doesn't guarantee that the distribution of the individual data (the number of sleep hours) in the population is normal.

It’s important to note two things: First, the idea of random sampling is to avoid bias and to have a representative sample of the population under study. Second, the rule of thumb is that the sample size should be approximately 30 or greater for the Central Limit Theorem to take effect, to provide a decent approximation of a normal distribution of sample means. In this instance, a sample size of 20 is close to 30, so we may anticipate that the sample mean distribution is roughly normal.

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A function is a rule that assigns exactly one output to a given input. The input is taken from a set called the domain, and the corresponding output belongs to a set called the range.

1. In this exercise, we're calling the pool of patients 1-8 the domain, and the pool of nurses A-D the range. The given table describes a function because any patient is assigned to only one nurse.

2. This wouldn't be a function if at least one patient was assigned to more than one nurse. If this were to happen in practice, the patient could be, say, given the same dose of some medicine twice if the nurses aren't careful.

3. Making the nurse pool the domain and the patient pool the range would give a relation that is not a function, since more than one patient is assigned to one nurse.

The equivalent expression to 16(w+q) is 16w + 16q, but none of the given options A, B, C, or D are correct as they do not accurately represent this distribution. The closest option would be C (16w + 9), though it is still incorrect because it has 9 instead of 16q.

The question asks which expression is equivalent to 16(w+q). The correct way to distribute a constant over a sum inside parentheses is to multiply each term inside the parentheses by that constant. So, 16 must be multiplied by both w and q.

Therefore, the equivalent expression is 16w + 16q. Looking at the provided options:

Since none of the given options are exactly 16w + 16q, no available option is a correct equivalent expression to 16(w+q).

Answer:

161 inches

Step-by-step explanation:

This problem is all about conversion. How many feet are in a yard? 3. How many feet are in 4 yards? 12 feet. There are 12 inches in a foot. 12 feet means 12 x 12 inches, which is 144. 144 + the other 17 inches, is 161.

Answer:

The answer is into the unkown

Step-by-step explanation:

elsa and anna are good sisters olaf olaf anna fiftys ahdpnf3oehisklNHW3q3tsqagwgdraw4gw

Answer:

Equation: 10+c=3

Answer: c=-7

Step-by-step explanation:

1. 10+c=3

2. c=3-10

3. c=-7

Answer:

c=-7

Step-by-step explanation:

c+10=3

Subtract 10 from both sides

c=-7

Choosing a green jelly bean.

Spinning a number less than 2 on a spinner.

Choosing a spade out of a standard deck of cards.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability of choosing a green jelly bean = number of green jelly bean / total number of beans

2/8 x 100 = 25%

Probability of spinning a number less than 2 on a spinner = number that is less than 2 / total number of sections

1/4 x 100 = 25%

Probability of choosing a choosing a spade= number of spade / total cards in the deck

13/54 x 100 = 25%

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The three options that have a probability of 25 percent are:

- Choosing a green jelly bean

- Spinning a number less than 2 on a spinner

- Choosing a spade from a standard deck of cards

The probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. A probability of 25 percent corresponds to a ratio of 1 out of 4 (since 25% is one-fourth of 100%). Let's analyze the options:

1. Choosing a green jelly bean: There are 2 green jelly beans out of a total of 2 + 1 + 5 = 8 jelly beans. The probability is 2/8, which simplifies to 1/4 or 25%. This option has a probability of 25%.

2. Rolling a number less than 3 on a six-sided die: There are 2 favorable outcomes (1 and 2) out of 6 possible outcomes (1 through 6). The probability is 2/6, which simplifies to 1/3 or approximately 33.33%. This option does not have a probability of 25%.

3. Spinning a number less than 2 on a spinner: There is 1 favorable outcome (1) out of 4 possible outcomes (1 through 4). The probability is 1/4 or 25%. This option has a probability of 25%.

4. Choosing an Oregon state quarter: There are 3 Oregon state quarters out of a total of 4 + 3 + 6 + 3 = 16 state quarters. The probability is 3/16, which is not equal to 25%.

5. Choosing a spade from a standard deck of cards: There are 13 spades out of a total of 13 + 13 + 13 + 13 = 52 cards. The probability is 13/52, which simplifies to 1/4 or 25%. This option has a probability of 25%.

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Answer:

[tex]P(X=x)=0.0004928[/tex]

Step-by-step explanation:

-This is a binomial probability problem.

-Given the probability of catching a cold is 0.03, n=6

#The probability of exactly 3 people catching a cold is calculated as:

[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X=3)={6\choose3}0.03^3(1-0.03)^3\\\\=0.0004928[/tex]

Hence, the probability of exactly 3 in 6 people catching a cold is 0.0004928

Answer:

Mean of sampling distribution = 25 inches

Standard deviation of sampling distribution = 4 inches

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 25 inches

Standard Deviation, σ = 12 inches

Sample size, n = 9

We are given that the distribution of length of the widgets is a bell shaped distribution that is a normal distribution.

a) Mean of the sampling distribution

The best approximator for the mean of the sampling distribution is the population mean itself.

Thus, we can write:

[tex]\bar{x} = \mu = 25\text{ inches}[/tex]

b) Standard deviation of the sampling distribution

[tex]s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{12}{\sqrt{9}} = 4\text{ inches}[/tex]

Using the Central Limit Theorem, it is found that:

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For the population:

Samples of size 9, thus [tex]n = 9[/tex].

By the Central Limit Theorem:

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