math quiz need help as soon as possible

Question

A certain group of test subjects had pulse rates with a mean of 84.7 beats per minute and a standard deviation of 11.3 beats per minute. Would it be unusual for one of the test subjects to have a pulse rate of 117.3 beats per minute?

Minimum​ "usual" visual equals ____ beats per minute

Is 117.3 beats per minute an unusual pulse​ rate and why?

Answer 1

Assuming that we are talking about a normal distribution, 95% of the test subjects have pulse rates between 84 - 2(11.3) and 84 + 2(11.3). That is, between 61.4 and 106.6.

Only 2.5% (half of 5%) of the test subjects have pulse rates above 106.6. The z-score for 117.3 is

(117.3 - 84.7)/ 11.3 ≈ 2.88 (nearly 3 standard deviations above the mean). So, a pulse rate of 117.3 is unusual.