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Answer:
1.74% probability that the commute takes more than 32 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:
a.What is the probability that the commute takes more than 32 minutes?
This is 1 subtracted by the pvalue of Z when X = 32. So:
has a pvalue of 0.9826.
So there is a 1-0.9826 = 0.0174 = 1.74% probability that the commute takes more than 32 minutes.