Suppose that resting pulse rates for healthy adults are found to follow a Normal distribution, with a mean of 69 beats per minute and a standard deviation of 9.5 beats per minute. What does it mean if Bonnie has a pulse rate of 78.5 beats per minute? a. Bonnie's pulse rate, when converted to a standard score, would be 1.5. b. Bonnie's pulse rate is two standard deviations above the mean. c. Approximately 32% of adults have pulse rates higher than Bonnie's. d. Approximately 16% of adults have pulse rates higher than Bonnie's.

Question

Mathematics

Chaim Howard

8 February, 10:20

Suppose that resting pulse rates for healthy adults are found to follow a Normal distribution, with a mean of 69 beats per minute and a standard deviation of 9.5 beats per minute. What does it mean if Bonnie has a pulse rate of 78.5 beats per minute? a. Bonnie's pulse rate, when converted to a standard score, would be 1.5. b. Bonnie's pulse rate is two standard deviations above the mean. c. Approximately 32% of adults have pulse rates higher than Bonnie's. d. Approximately 16% of adults have pulse rates higher than Bonnie's.

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Scarlett Harris · Answer 1

Approximately 16% of adults have a pulse rate higher than bonnie'.

Step-by-step explanation:

A normal random variable with mean Mu = 69 and standard deviation sd = 9.5 is standardized with the transformation:

Z = (X - Mu) / sd = (X - 69) / 9.5

For a pulse rate value of 78.5, Z = (78.5 - 69) / 9.5 = 1.0

P (X <78.5) = P (Z <1.0) = 0.8413.

P (X> 78.5) = P (Z> 1.0) = 0.1587.

The standard score for the Bonnie's pulse rate is 1.0.

Bonnie's pulse rate is at the 1.0 standard deviations above the mean.

Approximately 16% of adults have a pulse rate higher than bonnie'.