The distribution of times runs of Atheletes are normally distributed with the me

Question

The distribution of times runs of Atheletes are normally distributed with the mean of 40 and a standard deviation of 5.
A) What is the probability that an athlete will have a time greater than 50 ?
B) what is the probability that an athlete will have a time between 35 and 45?
Show detailed work and explanation. The distribution of times runs of Atheletes are normally distributed with the mean of 40 and a standard deviation of 5.
A) What is the probability that an athlete will have a time greater than 50 ?
B) what is the probability that an athlete will have a time between 35 and 45?
Show detailed work and explanation.
A) What is the probability that an athlete will have a time greater than 50 ?
B) what is the probability that an athlete will have a time between 35 and 45? A) What is the probability that an athlete will have a time greater than 50 ?
B) what is the probability that an athlete will have a time between 35 and 45?
Show detailed work and explanation.

Explanation / Answer

Mean is 40 and s is 5

z can be found as (x-mean)/s

a) P(x>50)=P(z>(50-40)/5)=P(z>2) or 1-P(z<2) which from the normal distribution table is 1-0.9772=0.0228

b) P(35<x<45)=P((35-40)/5<z<(45-40)/5)=P(-1<z<1) =2*P(z<1)-1 or 2*0.8413-1=0.6826

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