Question

A doctor wants to estimate the HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the HDL cholesterol within 2 points with 99 % confidence assuming sigma equals 14.2 question mark Suppose the doctor would be content with 90 % confidence. How does the decrease in confidence affect the sample size required? A 99% confidence level requires nothing subjects. (Round up to the nearest whole number as needed.) A 90 % confidence level requires nothing subjects. (Round up to the nearest whole number as needed.) How does the decrease in confidence affect the sample size required?

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.

The mean number of heart transplants performed per day in a country is about

sevenseven.

Find the probability that the number of heart transplants performed on any given day is (a) exactly

fivefive ,

(b) at least

eighteight ,

and (c) no more than

threethree.

(a)

P(55 )equals=nothing

(Round to three decimal places as needed.)

(b) P(at least

88 )equals=nothing

(Round to three decimal places as needed.)

(c) P(no more than

33 )equals=nothing

(Round to three decimal places as needed.)

Which of the events are unusual? Select all that apply.

A.

The event in part (a) is unusual.

B.

The event in part (b) is unusual.

C.

The event in part (c) is unusual.

Complete parts (a) and (b) using the probability distribution below.

The number of overtime hours worked in one week per employee

Overtime hours	0	1	2	3	4	5	6
Probability	0.0260.026	0.0780.078	0.1510.151	0.2860.286	0.2290.229	0.1410.141	0.0890.089 (a) Find the mean, variance, and standard deviation of the probability distribution. Find the mean of the probability distribution. muμequals=nothing (Round to one decimal place as needed.) Find the variance of the probability distribution. sigma squaredσ2equals=nothing (Round to one decimal place as needed.) Find the standard deviation of the probability distribution. sigmaσequals=nothing (Round to one decimal place as needed.) (b) Interpret the results in the context of the real-life situation. A. An employee works an average of 1.41.4 overtime hours per week with a standard deviation of approximately 3.43.4 hours. B. An employee works an average of 2.12.1 overtime hours per week with a standard deviation of approximately 1.41.4 hours. C. An employee works an average 3.43.4 of overtime hours per week with a standard deviation of approximately 55 hours. D. An employee works an average of 3.43.4 overtime hours per week with a standard deviation of approximately 1.41.4 hours.

Answer 1

Solution: A doctor wants to estimate the HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the HDL cholesterol within 2 points with 99 % confidence assuming sigma equals 14.2 question mark Suppose the doctor would be content with 90 % confidence. How does the decrease in confidence affect the sample size required?

Answer: A 99% confidence level requires:

Where:

is the critical value at 0.01 significance level and is

Therefore the 99% confidence level requires 336 subjects.

A 90 % confidence level requires nothing subjects.

Answer:

Where:

is the critical value at 0.1 significance level and is

Therefore the 90% confidence level requires 137 subjects.

How does the decrease in confidence affect the sample size required?

Answer: Decrease in confidence level will decrease the sample size required.

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.

The mean number of heart transplants performed per day in a country is about 7.

Find the probability that the number of heart transplants performed on any given day is

(a) exactly 5,

Answer: The given process follows poisson distribution with mean = 7

We have to find

Therefore

(b) P(at least 8 ) is

Answer: We have to find

We know that:

We can use excel to find using the below formula:

Therefore P(at least 8) = 0.401

(c) P(no more than 3 ) is

Answer: We have to find .

Using the below excel formula we have:

=POISSON(3,7,TRUE) = 0.082

Therefore the P(no more than 3) = 0.082

Which of the events are unusual? Select all that apply.

Answer: D) None of these events is unusual

The number of overtime hours worked in one week per employee

(a) Find the mean, variance, and standard deviation of the probability distribution.

Find the mean of the probability distribution.

Answer: The mean is given below:

Therefore the mean

rounded to one decimal place.

Find the variance of the probability distribution.

Answer: The variance of the probability distribution is:

Therefore:

  

Find the standard deviation of the probability distribution.

Answer: The standard deviation of the probability distribution is:

  

  

(b) Interpret the results in the context of the real-life situation.

Answer:

D. An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4

hours.