SOLUTION: Healthy people have body temperatures that are normally distributed with a mean of 98.20 ∘F and a standard deviation of 0.62 ∘F. (a) If a healthy person is randomly

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Question 1126828: Healthy people have body temperatures that are normally distributed with a mean of 98.20 ∘F and a standard deviation of 0.62 ∘F.
(a) If a healthy person is randomly selected, what is the probability that he or she has a temperature above 99.9 ∘F.
(b) A hospital wants to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 0.5 % of healthy people to exceed it?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Meanmu+=+98.2F
Standard Deviation delta=+.62F+
(a)
z%2899.2%29+=+%2899.2-98.2%29%2F0.62+=+1.6129
P%28x+%3E+00.2%29+=+P%28z%3E+1.6129%29+=+0.0534

(b)
Find the z-score that has a right tail of 5%:
z+=inv%280.95%29+=+1.645
x+=+z%28delta%29+%2B+mu+=+1.645%28.62%29+%2B+98.2+=99.2199=99.2