Question

Women have pulse rates that are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.7 beats per minute. Complete parts a through c below.

a. Find the percentiles Upper P 1 and Upper P 99.

b. A doctor sees exactly 35 patients each day. Find the probability that 35 randomly selected women have a mean pulse rate between 64 and 92 beats per minute. The probability is __.

c. If the doctor wants to select pulse rates to be used as cutoff values for determining when further tests should be​ required, which pulse rates are better to​ use: the results from part​ (a) or the pulse rates of 64 and 92 beats per minute from part​ (b)? Why?

A. Part​ (a), because the cutoff values should be based on individual patients rather than the mean pulse rate of the sample.

B. Part​ (b), because the cutoff values should be based on the mean pulse rate of the sample rather than individual patients.

C. Part​ (b), because the cutoff values should be based on individual patients rather than the mean pulse rate of the sample.

D. Both pulse rate ranges are equally acceptable.

Answer 1

a)

for 1th percentile critical value of z=		-2.326
therefore corresponding value P1=mean+z*std deviation=			50.29

for 99th percentile critical value of z=		2.326
therefore corresponding value P99=mean+z*std deviation=			104.71

b)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	77.5
std deviation   =σ=	11.7000
sample size       =n=	35
std error=σx̅=σ/√n=	1.9777

  probability that 35 randomly selected women have a mean pulse rate between 64 and 92 beats per minute:

probability =

P(64<X<92)

=

P(-6.83<Z<7.33)=

1-0=

1.0000

c

)A. Part​ (a), because the cutoff values should be based on individual patients rather than the mean pulse rate of the sample.