A doctor collects a large set of heart rate measurements that approximately follow a normal distribution. He only reports 3 statistics, the mean = 110 beats per minute, the minimum = 65 beats per minute, and the maximum = 155 beats per minute. Which of the following is most likely to be the standard deviation of the distribution?

A. 5

B. 15

C. 90

15

Step-by-step explanation:

We know that heart rate measurements are normally distributed with mean μ=110. We have to find standard deviation whereas minimum and maximum value of data are 65 and 155 beats per min.

We know that by the empirical rule, 99.7% of value lies within 3 standard deviation from the mean. We can see that 99.7% covers approximately all the data and we can assume that all the data lies within 3 standard deviation. Now we check for each value whether the interval μ±3*σ contains minimum value 65 and maximum value 155 beats per min or not.

A. 5

μ±3*σ

110±3*5

110±15

(95,125)

B. 15

μ±3*σ

110±3*15

110±45

(65,155)

We can see that for standard deviation=15, μ±3*σ contains minimum value=65 and maximum value=155.

C. 90

μ±3*σ

110±3*90

110±270

(-160,380)

Thus, the standard deviation of the distribution is most likely to be 15.