statistics multi-part question and need a sample draft to help me learn.

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:

?

n

p

X̄

σ

s

μ

N

X

= 234

?

X

p

X̄

n

N

μ

s

σ

= 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?

?

Yes

No

Why or why not? Check all that apply.

σ

IS KNOWN

POPULATION IS NOT NORMAL

N IS LESS THAN 30

N IS AT LEAST 30

POPULATION IS NORMAL

σ

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 answer

the starting salary

the mean starting salary of 32 randomly selected nurses

a randomly selected nurse

32 randomly selected nurses

all nurses

the mean starting salary of all nurses

The variable information collected from each individual is

Select an answer

the mean starting salary of 32 randomly selected nurses

all nurses

a randomly selected nurse

the starting salary

the mean starting salary of all nurses

32 randomly selected nurses

This variable is a

Select an answer

qualitative

qualitative — discrete

quantitative — continuous

variable.

The random variable X is as follows:

Select an answer

rv X = a randomly selected nurse

rv X = the mean starting salary of 32 randomly selected nurses

rv X = the starting salary of a randomly selected nurse

rv X = starting salary is normally distributed

rv X = the mean starting salary of all nurses

rv X = all nurses

b) List the givens with the correct symbols.

?

n

X

p

μ

X̄

σ

N

s

= 67694 dollars

?

σ

μ

X

n

N

s

p

X̄

= 10333 dollars

?

s

n

μ

σ

N

X̄

p

X

= 32

c) Identify the random variable

X

¯

in the context of this problem.

Select an answer

rv X̄ = the starting salary of a randomly selected nurse

rv X̄ = the starting salary of 32 randomly selected nurses

rv X̄ = the mean starting salary of 32 randomly selected nurses

rv X̄ = a randomly selected nurse

rv X̄ = the mean starting salary of all nurses

rv 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 answer

right-skewed

unknown

left-skewed

normal or approximately normal

uniform

Why? Check all that apply:

σ

IS UNKNOWN

N IS AT LEAST 30

σ

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 answer

Yes, the probability of having a sample mean starting salary of at least 72422.42 dollars is less than or equal to 0.05

Yes, the probability of having a sample mean starting salary of at least 72422.42 dollars is more than 0.05

Yes, the probability of having a sample mean starting salary of at most 72422.42 dollars is less than or equal to 0.05

Yes, the probability of having a sample mean starting salary of at most 72422.42 dollars is more than 0.05

No, the probability of having a sample mean starting salary of at least 72422.42 dollars is less than or equal to 0.05

No, the probability of having a sample mean starting salary of at least 72422.42 dollars is more than 0.05

No, the probability of having a sample mean starting salary of at most 72422.42 dollars is less than or equal to 0.05

No, 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 answer

There is no evidence that the mean starting salary of all nurses has changed from 67694 dollars

There is evidence that the mean starting salary of all nurses may now be higher than 67694 dollars

There 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 answer

the mean blood pressure of all people in China

a randomly selected person in China

the blood pressure

24 randomly selected people in China

the mean blood pressure of 24 randomly selected people in China

all people in China

The variable information collected from each individual is

Select an answer

the blood pressure

a randomly selected person in China

all people in China

24 randomly selected people in China

the mean blood pressure of 24 randomly selected people in China

the mean blood pressure of all people in China

This variable is a

Select an answer

qualitative

qualitative — discrete

quantitative — continuous

variable.

The random variable X is as follows:

Select an answer

rv X = the blood pressure of a randomly selected person in China

rv X = the mean blood pressure of all people in China

rv X = blood pressure is normally distributed

rv X = a randomly selected person in China

rv X = all people in China

rv X = the mean blood pressure of 24 randomly selected people in China

b) List the givens with the correct symbols.

?

s

X̄

p

μ

X

n

σ

N

= 128 mmHg

?

μ

X̄

p

X

σ

n

N

s

= 23 mmHg

?

X

N

n

p

σ

μ

s

X̄

= 24

c) Identify the random variable

X

¯

in the context of this problem.

Select an answer

rv X̄ = the mean blood pressure of all people in China

rv X̄ = blood pressure is normally distributed

rv X̄ = the blood pressure of 24 randomly selected people in China

rv X̄ = the mean blood pressure of 24 randomly selected people in China

rv X̄ = the blood pressure of a randomly selected person in China

rv 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 answer

uniform

unknown

normal or approximately normal

left-skewed

right-skewed

Why? Check all that apply:

POPULATION IS NOT NORMAL

σ

IS KNOWN

σ

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 answer

Yes, the probability of having a sample mean blood pressure of at least 138.89 mmHg is less than or equal to 0.05

Yes, the probability of having a sample mean blood pressure of at least 138.89 mmHg is more than 0.05

Yes, the probability of having a sample mean blood pressure of at most 138.89 mmHg is less than or equal to 0.05

Yes, the probability of having a sample mean blood pressure of at most 138.89 mmHg is more than 0.05

No, the probability of having a sample mean blood pressure of at least 138.89 mmHg is less than or equal to 0.05

No, the probability of having a sample mean blood pressure of at least 138.89 mmHg is more than 0.05

No, the probability of having a sample mean blood pressure of at most 138.89 mmHg is less than or equal to 0.05

No, 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 answer

There is no evidence that the mean blood pressure of all people in China has changed from 128 mmHg

There is evidence that the mean blood pressure of all people in China may now be higher than 128 mmHg

There 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 answer

the mean length of 18 randomly selected Atlantic cod

all Atlantic cod

the mean length of all Atlantic cod

18 randomly selected Atlantic cod

a randomly selected Atlantic cod

the length

The variable information collected from each individual is

Select an answer

all Atlantic cod

the length

the mean length of 18 randomly selected Atlantic cod

the mean length of all Atlantic cod

18 randomly selected Atlantic cod

a randomly selected Atlantic cod

This variable is a

Select an answer

qualitative

quantitative — continuous

qualitative — discrete

variable.

The random variable X is as follows:

Select an answer

rv X = the mean length of all Atlantic cod

rv X = all Atlantic cod

rv X = the mean length of 18 randomly selected Atlantic cod

rv X = a randomly selected Atlantic cod

rv X = the length of a randomly selected Atlantic cod

rv X = length is normally distributed

b) List the givens with the correct symbols.

?

n

X

σ

p

s

X̄

μ

N

= 49.9 cm

?

X̄

X

n

p

N

σ

s

μ

= 3.74 cm

?

σ

X̄

n

s

p

X

N

μ

= 18

c) Identify the random variable

X

¯

in the context of this problem.

Select an answer

rv X̄ = the mean length of all Atlantic cod

rv X̄ = the length of a randomly selected Atlantic cod

rv X̄ = a randomly selected Atlantic cod

rv X̄ = length is normally distributed

rv X̄ = the length of 18 randomly selected Atlantic cod

rv 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 answer

uniform

normal or approximately normal

unknown

right-skewed

left-skewed

Why? Check all that apply:

POPULATION IS NOT NORMAL

N IS LESS THAN 30

POPULATION IS NORMAL

σ

IS KNOWN

σ

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 answer

Yes, the probability of having a sample mean length of at least 51.53 cm is less than or equal to 0.05

Yes, the probability of having a sample mean length of at least 51.53 cm is more than 0.05

Yes, the probability of having a sample mean length of at most 51.53 cm is less than or equal to 0.05

Yes, the probability of having a sample mean length of at most 51.53 cm is more than 0.05

No, the probability of having a sample mean length of at least 51.53 cm is less than or equal to 0.05

No, the probability of having a sample mean length of at least 51.53 cm is more than 0.05

No, the probability of having a sample mean length of at most 51.53 cm is less than or equal to 0.05

No, 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 answer

There is no evidence that the mean length of all Atlantic cod has changed from 49.9 cm

There is evidence that the mean length of all Atlantic cod may now be higher than 49.9 cm

There is evidence that the mean length of all Atlantic cod may now be lower than 49.9 cm

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November 28, 2023

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