The number of pedestrians crossing a street in downtown Providence during the morning rush hour is assumed to follow a normal distribution with mean 290 and standard deviation 50. a. What is the probability of more than 250 pedestrians crossing the street?

78.81% probability of more than 250 pedestrians crossing the street

Step-by-step explanation:

Problems of normally distributed samples are 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 of more than 250 pedestrians crossing the street?

This is 1 subtracted by the pvalue of Z when X = 250. So

has a pvalue of 0.2119

1 - 0.2119 = 0.7881

78.81% probability of more than 250 pedestrians crossing the street

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