Using the normal distribution, it is found that there is a 0.963 = 96.3% probability that on a given day, his commute will be longer than 49 minutes.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, the mean and the standard deviation are given, respectively, by:
.
The probability that on a given day, his commute will be longer than 49 minutes is <u>one subtracted by the p-value of Z when X = 49</u>, hence:
Z = -1.78
Z = -1.78 has a p-value of 0.0375.
1 - 0.0375 = 0.963.
0.963 = 96.3% probability that on a given day, his commute will be longer than 49 minutes.
More can be learned about the normal distribution at brainly.com/question/24663213
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