Question

In: Statistics and Probability

Women have pulse rates that are normally distributed with a mean of 77.5 beats per minute...

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.

Solutions

Expert Solution

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=σ=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.


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