Question

John drives to work each morning, and the trip takes an average of µ = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, what is the probability that John’s drive to work will take less than 35 minutes?​

Answer 1

Answer: 0.2742531

Explanation:

Let x denote the random variable that represents the driving times.

As per given we have,

`\mu = 38`

`\sigma = 5`

Z-score value corresponds to x= 35,

`z=(x-\mu)/(\sigma)=(35-38)/(5)=-0.6`

Using z-value table ,

The probability that John’s drive to work will take less than 35 minutes:-

P(X<35)=P(z<-0.6)=1-P(z<0.6)=1-0.7257469=0.2742531

hence, the required probability = 0.2742531