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Probability: Systolic Blood Pressure

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Assume that the mean systolic blood pressure of normal adults is 120 millimeters of mercury (mm Hg) and the standard deviation is 5.6. Assume the variable is normally distributed.

A.) If an individual is selected at random, find the probability that the person's pressure will be between 118 and 121.8mm Hg.

B.) If a sample of 30 adults is selected at random, find the probability that their mean pressure will be between 118 and 121.8mm Hg.

Solution Summary

The solution assumes that the mean systolic blood pressure of normal adults is 120 millimeters of mercury (mm Hg) and the standard deviation is 5.6. Assume the variable is normally distributed. Standard normal tables are examined.

Solution Preview

Let X be the systolic blood pressure of normal adults. According to hypothesis we know X~N(120,5.6^2).
Since Y=(X-120)/5.6~N(0,1) standard normal distribution, let F(y) be the standard normal distribution function.
Note. F(y)+F(-y)=1

(1) ...

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• BSc , Wuhan Univ. China
• MA, Shandong Univ.
Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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