Question

2-30 Assume that heathy human body on temperature are normally distributed with a mean of 98.20F and a standard dev- ·lation of 0.62F. Belelve Bellevue Hospital in new york city uses 100.6F as the normal threshold for people who are too hot (fever) What percentange of normal people would be considered to have a fever using the threshold?

Answer 1

1)

X ~ N ( µ = 98.2 , σ = 0.62 )
We covert this to standard normal as
P ( X < x) = P ( (Z < X - µ ) / σ )
P ( X > 100.6 ) = P(Z > (100.6 - 98.2 ) / 0.62 )
= P ( Z > 3.87 )
= 1 - P ( Z < 3.87 )
= 1 - 0.9999

= 0.0001

2)

X ~ Bin ( n, p)

Where n = 6 , p= 0.1

Binomial probabiltiy distribution is

P(X) = nCx px ( 1 - p)n-x

P(X = 2) = 6C2 * 0.12 * ( 1 - 0.1)4

= 0.0984