Question

Assume that females have pulse rates that are normally distributed with a mean of mu equals 73.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 77 beats per minute If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 77 beats per minute

Answer 1

a)

Given,

= 73 , = 12.5

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

P(X < 77) = P(Z < (77 - 73) / 12.5)

= P(Z < 0.32)

= 0.6255

b)

Using central limit theorem,

P( < x) = P(Z < ( x - ) / ( / sqrt(n) ) )

P( < 77) = P(Z < (77 - 73) / (12.5 / sqrt(25) ) )

= P(Z < 1.6)

= 0.9452