MEASURE OF CENTRAL TENDENCY

Question

The pulse rate of a normal distribution of healthy males have a mean of 72 beats per minute, and a standard deviation of 3.t beats per minute,what percentage of Individuals have a pulse rate differ by 2 beats from the mean

Answer 1

Let x = rate, to be within 2 of mean (72), would have to be between 70 and 74.

Find P(70 < x < 74)

Knowing z = (x - mean/SD) has normal distribution mean 0 SD = 1:

P(70 < x < 74) = P( (70 - 72)/3.1 < z < (74 - 72)/3.1) = P(-0.645 < z < 0.645) = P(z < 0.645) - P(z < -0.645) = 0.7405 - 0.2595 = 0.481