Assume that the random variable X is normally distributed, with mean mu equals 80μ=80 and standard deviation sigma equals 20.σ=20. Compute the probability P(Xgreater than>9696).

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:

Compute the probability P(Xgreater than>96).

This is 1 subtracted by the pvalue of Z when X = 96. So

has a pvalue of 0.7881