Question

Assume that females have pulse rates that are normally distributed with a mean of

mu equals 76.0?=76.0

beats per minute and a standard deviation of

sigma equals 12.5?=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

7979

beats per minute.The probability is

nothing.

?(Round to four decimal places as? needed.)

b. If

44

adult females are randomly? selected, find the probability that they have pulse rates with a mean less than

7979

beats per minute.The probability is

nothing.

?(Round to four decimal places as? needed.)

c. Why can the normal distribution be used in part? (b), even though the sample size does not exceed? 30?

A.

Since the mean pulse rate exceeds? 30, the distribution of sample means is a normal distribution for any sample size.

B.

Since the original population has a normal? distribution, the distribution of sample means is a normal distribution for any sample size.

C.

Since the distribution is of sample? means, not? individuals, the distribution is a normal distribution for any sample size.

D.

Since the distribution is of? individuals, not sample? means, the distribution is a normal distribution for any sample size.

Answer 1

a)

Given,

= 76, = 12.5

We convert this to standard normal as

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

Therefore,

P( X < 79) = P( Z < 79 - 76 / 12.5)

= P( Z < 0.24)

= 0.5948

b)

The central limit theorem is

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

So,

P( < 79) = P( Z < 79 - 76 / 12.5 / sqrt(4) )

= P( Z < 0.48)

= 0.6844

c)

The normal distribution is used in part(b),

Since the original population has a normal distribution, the distribution of sample mean is a

normal distribution for any sample size .