College

The weight of adults in a certain state follows an approximately normal distribution with a mean of 150 pounds and a standard deviation of 17 pounds. According to the empirical rule, what percent of adults weigh more than 116 pounds?

Answer :

Answer:

97.5%

Step-by-step explanation:

Find the z-score:

z = (x − μ) / σ

z = (116 − 150) / 17

z = -2

According to the empirical rule, 95% of a population are between -2 and +2 standard deviations. That means that half of that, or 47.5%, are between -2 and 0 standard deviations. Since 50% are greater than 0 standard deviations, the total probability is 47.5% + 50%, or 97.5%.

P(Z > -2) = P(-2 < Z < 0) + P(Z > 0)

P(Z > -2) = 47.5% + 50%

P(Z > -2) = 97.5%

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