The time it takes to travel from my apartment to work is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability that my commute time tomorrow will take between 30 and 35 minutes?

13.59% probability that my commute time tomorrow will take between 30 and 35 minutes

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

What is the probability that my commute time tomorrow will take between 30 and 35 minutes?

This is the pvalue of Z when X = 35 subtracted by the pvalue of Z when X = 30. So

X = 35

has a pvalue of 0.9772

X = 30

has a pvalue of 0.8413

0.9772 - 0.8413 = 0.1359

13.59% probability that my commute time tomorrow will take between 30 and 35 minutes

The solution is and

Step-by-step explanation:

The expression is

Multiplying the term by , we get,

Adding both sides by 1,

Taking factor, we get,

Equating the factors to 0,

and

Thus, the smaller value is

The solution is and