empirical rule-standard deviation

Question

Suppose that diastolic blood pressure readings of adult males have a bell-shaped distribution with a mean of 82 mmHg and a standard deviation of 12 mmHg. Using the empirical rule, what percentage of adult males have diastolic blood pressure readings that are no more than 46 mmHg? Please do not round your answer.

Answer 1

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Answer 2

mean = 82, standard deviation =12

P(x</=46)= 0.15%

find the z score for 46

z = (46-82)/12 = -36/12 = -3

by the empirical rule 99.7% are within 3 standard deviations from the mean

the remaining .3% are half in each tail of the normal distribution

leaving .3%/2 = .15% = P(x</=46)

Probability of at most 46 is equal to the probability of less than or equal to 46