Question

Assume that females have pulse rates that are normally distributed with a mean of mu equals 76.0 μ=76.0 beats per minute and a standard deviation of sigma equals 12.5 σ=12.5 beats per minute. Complete parts​ (a) through​ (c) below. a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 83 83 beats per minute. The probability is . 7123 .7123. ​(Round to four decimal places as​ needed.) b. If 16 16 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 83 83 beats per minute. The probability is nothing . ​(Round to four decimal places as​ needed.)

Answer 1

a)

Given

= 76 , = 12.5

We convert this to standard normal as

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

So,

P (X < 83) = P( Z < 83 - 76 / 12.5)

= P( Z < 0.56)

0.7123

b)

Using central limit theorem,

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

So

P( < 83) = P( Z < 83 - 76 / 12.5 / sqrt(16) )

= P( Z < 2.24)

= 0.9875