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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?​

Respuesta :

Answer:

The probability that John’s drive to work will take less than 35 minutes is 0.2743

Step-by-step explanation:

Given : [tex]\mu = 38 \\\sigma = 5[/tex]

To Find :what is the probability that John’s drive to work will take less than 35 minutes?​

Solution:

[tex]\mu = 38 \\\sigma = 5[/tex]

We are supposed to find P(x<35)

We will use z score

Formula: [tex]z=\frac{x-\mu}{\sigma}[/tex]

Substitute x = 35

[tex]z=\frac{35-38}{5}[/tex]

z= −0.6

Refer the z table for p value

P(x<35)= 0.2743

Hence the probability that John’s drive to work will take less than 35 minutes is 0.2743