Question

Assume that females have pulse rates that are normally distributed with a mean of mu equals 76.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts​ (a) through​ (b) below.

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 82 beats per minute.

The probability is __________.

b. If 4 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 82 beats per minute.

The probability is ___________ .

Answer 1

Solution :

Given that ,

mean = = 76.0

standard deviation = = 12.5

(a)

n = 1

= 76.0 and

= / n = 12.5 / 1 = 12.5

P( < 82) = P(( - ) / < (82 - 76) / 12.5)

= P(z < 0.48)

Using standard normal table,

P( < 82) = 0.6844

Probability = 0.6844

(b)

n = 4

= 76 and

= / n = 12.5 / 4 = 12.5 / 2 = 6.25

P( < 82) = P(( - ) / < (82 - 76) / 6.25)

= P(z < 0.96)

Using standard normal table,

P( < 82) = 0.8315

Probability = 0.8315