Assume the random variable X is normally distributed, with mean 46 and standard deviation 8. Find the 7 th percentile.

The 7th percentile is 34.2

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:

Find the 7 th percentile.

The value of X when Z has a pvalue of 0.07. So it is X when Z = -1.475.

The 7th percentile is 34.2

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