# Normal Distribution; Mean; Standard Deviation Functions

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I am having trouble with PART B of this problem.

Here is the whole problem:

Assume body temperatures are normally distributed with mean of 98.2 and a standard dev. of 0.62

Part A) Assuming a hospital defines a fever as 100 or over, determine the percentage of a normal healthy person considered to have a fever using Z table

Answer: 100-98.2/.62=2.90=.19% rounded.

*Part B) I have the procedure right but I can't get the right answer. z=x-u/o Determine the minimum fever if doctors at the hospital want only 3.0% of healthy persons to be diagnosed as having a fever. Use closest z score. Answer is 99.37.

Another part B, different problem. How does 100.1-98.2/.62=.11 in part A and part B = 99.55 wanting 1.5% of healthy to be diagnosed?

A different B: 99.2-98.2/.62=5.37 for part A, and B wanting 2.5% = 99.42.?? I have been taking 1-the %s (3.0%, 2.5% et cetera as above) but I'm still not getting the right answers.

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##### Solution Summary

The expert examines normal distribution mean and standard deviation functions. The procedures for diagnosing a person with a fever is determined.

###### Education

- 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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