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A random variable X is normally distributed. It has a mean of 234 and a standard deviation of 22.

List the givens with correct symbols:

?npX̄σsμNX = 234

?XpX̄nNμsσ = 22

a) If you take a sample of size 12, can you say what the shape of the sampling distribution for the sample mean is?

?YesNo

Why or why not? Check all that apply.

• $\sigma$ is known
• population is not normal
• n is less than 30
• n is at least 30
• population is normal
• $\sigma$ is unknown

b) For a sample of size 12, state the mean and the standard deviation of the sampling distribution of the sample mean.

mean of the sampling distribution of the sample mean when n = 12:

standard deviation of the sampling distribution of the sample mean when n = 12:

Round final answer to two decimal places

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Question 2

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The mean starting salary for nurses is 67,694 dollars nationally. The standard deviation is approximately 10,333 dollars. The starting salary is not normally distributed. A sample of 32 starting salaries for nurses is taken.

It is possible with rounding for a probability to be 0.0000.

a) Identify the individual, variable, type of variable and the random variable X in the context of this problem.

The individual is

Select an answerthe starting salarythe mean starting salary of 32 randomly selected nursesa randomly selected nurse32 randomly selected nursesall nursesthe mean starting salary of all nurses

The variable information collected from each individual is Select an answerthe mean starting salary of 32 randomly selected nursesall nursesa randomly selected nursethe starting salarythe mean starting salary of all nurses32 randomly selected nurses

This variable is a Select an answerqualitativequalitative — discretequantitative — continuous variable.

The random variable X is as follows:

Select an answerrv X = a randomly selected nurserv X = the mean starting salary of 32 randomly selected nursesrv X = the starting salary of a randomly selected nurserv X = starting salary is normally distributedrv X = the mean starting salary of all nursesrv X = all nurses

b) List the givens with the correct symbols.

?nXpμX̄σNs = 67694 dollars

?σμXnNspX̄ = 10333 dollars

?snμσNX̄pX = 32

c) Identify the random variable

$\overline{X}$ in the context of this problem.

Select an answerrv X̄ = the starting salary of a randomly selected nurserv X̄ = the starting salary of 32 randomly selected nursesrv X̄ = the mean starting salary of 32 randomly selected nursesrv X̄ = a randomly selected nurserv X̄ = the mean starting salary of all nursesrv X̄ = starting salary is normally distributed

d) Find the mean of the sampling distribution of the sample mean.

Put the numeric value in the first box and the correct units in the second box.

e) Find the standard deviation of the sampling distribution of the sample mean.

Put the numeric value rounded to two decimal places in the first box and the correct units in the second box.

f) What is the shape of the sampling distribution of the sample mean?

Select an answerright-skewedunknownleft-skewednormal or approximately normaluniform

Why? Check all that apply:

• $\sigma$ is unknown
• n is at least 30
• $\sigma$ is known
• n is less than 30
• population is not normal
• population is normal

g) Find the probability that the sample mean starting salary of the 32 randomly selected nurses is less than 66726.1 dollars.

Round final answer to 4 decimal places.

h) Find the probability that the sample mean starting salary of the 32 randomly selected nurses is more than72422.42 dollars.

Round final answer to 4 decimal places.

i) Is a mean starting salary of 72422.42 dollars unusually high for 32 randomly selected nurses?

Select an answerYes, the probability of having a sample mean starting salary of at least 72422.42 dollars is less than or equal to 0.05Yes, the probability of having a sample mean starting salary of at least 72422.42 dollars is more than 0.05Yes, the probability of having a sample mean starting salary of at most 72422.42 dollars is less than or equal to 0.05Yes, the probability of having a sample mean starting salary of at most 72422.42 dollars is more than 0.05No, the probability of having a sample mean starting salary of at least 72422.42 dollars is less than or equal to 0.05No, the probability of having a sample mean starting salary of at least 72422.42 dollars is more than 0.05No, the probability of having a sample mean starting salary of at most 72422.42 dollars is less than or equal to 0.05No, the probability of having a sample mean starting salary of at most 72422.42 dollars is more than 0.05

j) If you found a mean starting salary for a sample of 32 nurses as high as 72422.42 dollars, what might you conclude?

Select an answerThere is no evidence that the mean starting salary of all nurses has changed from 67694 dollarsThere is evidence that the mean starting salary of all nurses may now be higher than 67694 dollarsThere is evidence that the mean starting salary of all nurses may now be lower than 67694 dollars

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Question 3

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According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg. Blood pressure is normally distributed. Suppose a sample of size 24 is taken.

It is possible with rounding for a probability to be 0.0000.

a) Identify the individual, variable, type of variable and the random variable X in the context of this problem.

The individual is Select an answerthe mean blood pressure of all people in Chinaa randomly selected person in Chinathe blood pressure24 randomly selected people in Chinathe mean blood pressure of 24 randomly selected people in Chinaall people in China

The variable information collected from each individual is Select an answerthe blood pressurea randomly selected person in Chinaall people in China24 randomly selected people in Chinathe mean blood pressure of 24 randomly selected people in Chinathe mean blood pressure of all people in China

This variable is a

Select an answerqualitativequalitative — discretequantitative — continuous variable.

The random variable X is as follows:

Select an answerrv X = the blood pressure of a randomly selected person in Chinarv X = the mean blood pressure of all people in Chinarv X = blood pressure is normally distributedrv X = a randomly selected person in Chinarv X = all people in Chinarv X = the mean blood pressure of 24 randomly selected people in China

b) List the givens with the correct symbols.

?sX̄pμXnσN = 128 mmHg

?μX̄pXσnNs = 23 mmHg

?XNnpσμsX̄ = 24

c) Identify the random variable

$\overline{X}$ in the context of this problem.

Select an answerrv X̄ = the mean blood pressure of all people in Chinarv X̄ = blood pressure is normally distributedrv X̄ = the blood pressure of 24 randomly selected people in Chinarv X̄ = the mean blood pressure of 24 randomly selected people in Chinarv X̄ = the blood pressure of a randomly selected person in Chinarv X̄ = a randomly selected person in China

d) Find the mean of the sampling distribution of the sample mean.

Put the numeric value in the first box and the correct units in the second box.

e) Find the standard deviation of the sampling distribution of the sample mean.

Put the numeric value rounded to two decimal places in the first box and the correct units in the second box.

f) What is the shape of the sampling distribution of the sample mean?

Select an answeruniformunknownnormal or approximately normalleft-skewedright-skewed

Why? Check all that apply:

• population is not normal
• $\sigma$ is known
• $\sigma$ is unknown
• population is normal
• n is less than 30
• n is at least 30

g) Find the probability that the sample mean blood pressure of the 24 randomly selected people in China is less than 123.8 mmHg.

Round final answer to 4 decimal places.

DO NOT use the rounded standard deviation from part e in this computation.

Use the EXACT value of the standard deviation with the square root.

h) Find the probability that the sample mean blood pressure of the 24 randomly selected people in China is more than 138.89 mmHg.

Round final answer to 4 decimal places.

DO NOT use the rounded standard deviation from part e in this computation.

Use the EXACT value of the standard deviation with the square root.

i) Is a mean blood pressure of 138.89 mmHg unusually high for 24 randomly selected people in China?

Select an answerYes, the probability of having a sample mean blood pressure of at least 138.89 mmHg is less than or equal to 0.05Yes, the probability of having a sample mean blood pressure of at least 138.89 mmHg is more than 0.05Yes, the probability of having a sample mean blood pressure of at most 138.89 mmHg is less than or equal to 0.05Yes, the probability of having a sample mean blood pressure of at most 138.89 mmHg is more than 0.05No, the probability of having a sample mean blood pressure of at least 138.89 mmHg is less than or equal to 0.05No, the probability of having a sample mean blood pressure of at least 138.89 mmHg is more than 0.05No, the probability of having a sample mean blood pressure of at most 138.89 mmHg is less than or equal to 0.05No, the probability of having a sample mean blood pressure of at most 138.89 mmHg is more than 0.05

j) If you found a mean blood pressure for a sample of 24 people in China as high as 138.89 mmHg, what might you conclude?

Select an answerThere is no evidence that the mean blood pressure of all people in China has changed from 128 mmHgThere is evidence that the mean blood pressure of all people in China may now be higher than 128 mmHgThere is evidence that the mean blood pressure of all people in China may now be lower than 128 mmHg

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The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm. Assume the length of fish is normally distributed. A sample of 18 fish was taken.

It is possible with rounding for a probability to be 0.0000.

a) Identify the individual, variable, type of variable and the random variable X in the context of this problem.

The individual is Select an answerthe mean length of 18 randomly selected Atlantic codall Atlantic codthe mean length of all Atlantic cod18 randomly selected Atlantic coda randomly selected Atlantic codthe length

The variable information collected from each individual is Select an answerall Atlantic codthe lengththe mean length of 18 randomly selected Atlantic codthe mean length of all Atlantic cod18 randomly selected Atlantic coda randomly selected Atlantic cod

This variable is a Select an answerqualitativequantitative — continuousqualitative — discrete variable.

The random variable X is as follows:

Select an answerrv X = the mean length of all Atlantic codrv X = all Atlantic codrv X = the mean length of 18 randomly selected Atlantic codrv X = a randomly selected Atlantic codrv X = the length of a randomly selected Atlantic codrv X = length is normally distributed

b) List the givens with the correct symbols.

?nXσpsX̄μN = 49.9 cm

?X̄XnpNσsμ = 3.74 cm

?σX̄nspXNμ = 18

c) Identify the random variable

$\overline{X}$ in the context of this problem.

Select an answerrv X̄ = the mean length of all Atlantic codrv X̄ = the length of a randomly selected Atlantic codrv X̄ = a randomly selected Atlantic codrv X̄ = length is normally distributedrv X̄ = the length of 18 randomly selected Atlantic codrv X̄ = the mean length of 18 randomly selected Atlantic cod

d) Find the mean of the sampling distribution of the sample mean.

Put the numeric value in the first box and the correct units in the second box.

e) Find the standard deviation of the sampling distribution of the sample mean.

Put the numeric value rounded to two decimal places in the first box and the correct units in the second box.

f) What is the shape of the sampling distribution of the sample mean?

Select an answeruniformnormal or approximately normalunknownright-skewedleft-skewed

Why? Check all that apply:

• population is not normal
• n is less than 30
• population is normal
• $\sigma$ is known
• $\sigma$ is unknown
• n is at least 30

g) Find the probability that the sample mean length of the 18 randomly selected Atlantic cod is less than 51.3 cm.

Round final answer to 4 decimal places.

DO NOT use the rounded standard deviation from part e in this computation.

Use the EXACT value of the standard deviation with the square root.

h) Find the probability that the sample mean length of the 18 randomly selected Atlantic cod is more than51.53 cm.

Round final answer to 4 decimal places.

DO NOT use the rounded standard deviation from part e in this computation.

Use the EXACT value of the standard deviation with the square root.

i) Is a mean length of 51.53 cm unusually high for 18 randomly selected Atlantic cod?

Select an answerYes, the probability of having a sample mean length of at least 51.53 cm is less than or equal to 0.05Yes, the probability of having a sample mean length of at least 51.53 cm is more than 0.05Yes, the probability of having a sample mean length of at most 51.53 cm is less than or equal to 0.05Yes, the probability of having a sample mean length of at most 51.53 cm is more than 0.05No, the probability of having a sample mean length of at least 51.53 cm is less than or equal to 0.05No, the probability of having a sample mean length of at least 51.53 cm is more than 0.05No, the probability of having a sample mean length of at most 51.53 cm is less than or equal to 0.05No, the probability of having a sample mean length of at most 51.53 cm is more than 0.05

j) If you found a mean length for a sample of 18 Atlantic cod as high as 51.53 cm, what might you conclude?

Select an answerThere is no evidence that the mean length of all Atlantic cod has changed from 49.9 cmThere is evidence that the mean length of all Atlantic cod may now be higher than 49.9 cmThere is evidence that the mean length of all Atlantic cod may now be lower than 49.9 cm