Question

​john's commute time to work during the week follows the normal probability distribution with a mean time of 26.7 minutes and a standard deviation of 5.1 minutes. what is the probability that the commute time for a randomly selected day will be between 28 and 34​ minutes?

Answer 1

To evaluate the probability that a randomly selected day will be between 28 and 34 minutes we proceed as follows:
P(28<x<34)
First we evaluate the z-score for the above values:
z=(x-σ)/μ
μ=26.7
σ=5.1

when:
x=28
z=(28-26.7)/5.1
z=0.26
P(z<0.26)=0.6026

when x=34
z=(34-26.7)/5.1
z=1.43
P(z<1.43)=0.9236
hence:
P(28<x<34)=0.9236-0.6026=0.321~32.1%