Question

Assume that females have pulse rates that are normally distributed with a mean of mu equals 74.0 beats per minute and a standard deviation of sigma equals 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 81 beats per minute. The probability is nothing . ​(Round to four decimal places as​ needed.) b. If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 81 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. Click to select your answer(s).

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	74
std deviation   =σ=	12.5000

probability =

P(X<81)

=

P(Z<0.56)=

0.7123

b)

sample size       =n=	25
std error=σx̅=σ/√n=	2.5000

probability =

P(X<81)

=

P(Z<2.8)=

0.9974

c)

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