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Based on data from the National Health Survey, women between the ages of 18and 24have an average systolic blood pressures (in mm Hg) of 114.8with a standard deviation of 13.1. Systolic blood pressure for women between the ages of 18to 24follow a normal distribution.

a. If one woman from this population is randomly selected, find the probability that her systolic blood pressure is greater than 120.

b. If40women from this population are randomly selected, find the probability that their mean systolic blood pressure is greater than 120.

c. If the sample were four women between the ages of18to 24 and we did not know the original distribution, could the central limit theorem be used?

Short Answer

Expert verified

(a)P(X>120)=.3458

(b)P(X>120)=.558

(c)The central limit theorem cannot be used, because sample size 4is small and also the original distribution is not known.

Step by step solution

01

Given information (part a) 

Given in the question that, Based on data from the National Health Survey, women between the ages of 18and24have an average systolic blood pressures (in mm Hg) of 114.8with a standard deviation of13.1.Systolic blood pressure for women between the ages of 18to 24follow a normal distribution.

02

Explanation(part a)

According to the supplied details, the average blood pressure of women aged between18and 24years is 144.8mmhgwith a standard deviation of 13.1.

To estimate the probability of systolic blood pressure P(X>120), utilize the Ti-83 calculator. For this, click on 2nd, then DISTR, and then scroll down to the normalcdf option and enter the provided details. After this, click on ENTER button on the calculator to have the desired result. The screenshot is given below:

Therefore, the value probability thatP(X>120)is:

=1.6542

=.3458

03

Final answer(part a)

Required probability P(X>120)=.3458

04

Given information(part b)

Given in the question that, Based on data from the National Health Survey, women between the ages of 18and 24have an average systolic blood pressures (in mm Hg) of 114.8 with a standard deviation of 13.1. Systolic blood pressure for women between the ages of 18to24 follow a normal distribution.

05

Explanation(part b)

According to the provided details, the average blood pressure of women ages between18and 24years is 144.8mmhgwith a standard deviation 13.1.

To estimate the probability of40women's systolic blood pressure P(X¯>120), use the Ti-83 calculator. For this, click on 2nd, then DISTR, and then scroll down to the normalcdf option and enter the provided details. After this, click on ENTER button on the calculator to have the desired result. The screenshot is given below:

Therefore, the value probability that P(X>120)is:

=1-.4420

=.558

06

Final answer(part b)

Required probabilityP(X>120)=.558

07

Given information (part c) 

Given in the question that, Based on data from the National Health Survey, women between the ages of 18and24have an average systolic blood pressures (in mm Hg) of 114.8with a standard deviation of 13.1. Systolic blood pressure for women between the ages of 18to 24follow a normal distribution.

08

Explanation(part c)

According to the provided details, the average blood pressure of women ages between 18and 24years is 144.8mmhgwith a standard deviation 13.1.

The central limit theorem cannot be used, because sample size4 is small and also the original distribution is not known.

09

Final answer(part c)

The central limit theorem cannot be used, because sample size 4is small and also the original distribution is not known.

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