Question

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

Assume that females have pulse rates that are normally distributed with a mean of
mu equals 75.0?=75.0
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
8282
beats per minute.
The probability is
. 7123.7123.
?(Round to four decimal places as? needed.)
b. If
2525
adult females are randomly? selected, find the probability that they have pulse rates with a mean less than
8282
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 distribution is of sample? means, not? individuals, the distribution 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? individuals, not sample? means, the distribution is a normal distribution for any sample size.
D.
Since the mean pulse rate exceeds? 30, the distribution of sample means is a normal distribution for any sample size.

Homework Answers

Answer #1

a)

Given = 75, = 12.5

We convert this to standard normal as

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

So,

P( X < 82) = P( Z < 82 - 75 / 12.5)

= P( Z < 0.56)

= 0.7123

b)

The central limit theorem is

P( < x) = P(Z <  x - / / sqrt(n) )

So,

P( < 82) = P( Z < 82 - 75 / 12.5 / sqrt(25) )

= P( Z < 2.8)

= 0.9974

c)

Normal distribution is used in part b) because,

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

normal distribution for any sample size.

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