Question

Women have pulse rates that are normally distributed with a mean of 71.4 beats per minute and a standard deviation of 11.7 beats per minute. Complete parts a through c below. a. Find the percentiles Upper P 1 and Upper P 99. Upper P 1equals nothing beats per minute ​(Round to one decimal place as​ needed.)

Answer 1

Solution :

mean = = 71.4

standard deviation = = 11.7

Using standard normal table,

(a)

Upper P1

P(Z > z) = 1%

1 - P(Z < z) = 0.01

P(Z < z) = 1 - 0.01 = 0.99

P(Z < 2.33) = 0.99

z = 2.33

Using z-score formula,

x = z * + = 2.33 * 11.7 + 71.4 = 98.661

Upper P₁ = 98.7

Upper P99

P(Z > z) = 99%

1 - P(Z < z) = 0.99

P(Z < z) = 1 - 0.99 = 0.01

P(Z < -2.33) = 0.01

z = -2.33

Using z-score formula,

x = z * + = -2.33 * 11.7 + 71.4 = 44.139

Upper P₉₉ = 44.1