A certain group of test subjects had pulse rates with a mean of 80.1 beats per minute and a standard deviation of 10.5 beats per minute.

Question

A certain group of test subjects had pulse rates with a mean of 80.1 beats per minute and a standard deviation of 10.5 beats per minute. Would it be unusual for one of the test subjects to have a pulse rate of 141.1 beats per​ minute?

Maximum​ "usual" value= ______ beats per minute

​(Type an integer or a​ decimal.)

Answer 1

unusual would be a value of pulse rate (x) that is 2 standard deviations above the mean.

z -score for x would be the number of standard deviations above or below the mean

z-score = (x - mean)/standard deviation

for x = 141.1, mean = 80.1 and standard deviation = 10.5

z = (141.1 - 80.1)/10.5 = 5.8

so value of 141.1 is 5.8 standard deviations above the mean which would be very unusual.

max usual value is 2 standard deviations above the mean, so value of x that corresponds to 2 standard deviations above the mean has z score = 2, so

2 = (x - 80.1)/10.5

x = 101.7 is the maximum usual value.