A set of data following a normal distribution has a mean of 192.3 and a standard deviation of 11.8. Find the probability that a randomly selected value is less than 212.5

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Mathematics

19 August, 13:03

A set of data following a normal distribution has a mean of 192.3 and a standard deviation of 11.8. Find the probability that a randomly selected value is less than 212.5

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Cora Camacho · Answer 1

Answer: 95.64% of the values will be below 212.5 in our set of data.

First, determine the z-score for the expected value of 212.5. The z-score is the number of standard deviations that it is above or below the mean.

(212.5 - 192.3) / 11.8 = 1.71

A score of 212.5 is 1.71 standard deviations above the mean. Now, use a table to find the probability for a z-score of 1.71. The percent is 95.64%.