This Question: 1pt 9 of 20 (3 complete) This Test: 20 pts possible Women have pu

Question

This Question: 1pt 9 of 20 (3 complete) This Test: 20 pts possible Women have pulse rates that are normalily dsthbuted with a mean of 7e7 beats per minute and a standard doviation of 112 beats per minute Complote viation of 11.2 beats per minute. Complete parts a through c below a. Find the percentiles P, and Pgs P,- beats per minute Round to one decimal place as needed.) (Round to one decimal place as needed.) b. A doctor sees exactly 45 patients each day. Find the probabity that 45 randomly selected women have a mean pulse rate between 65 and 89 beats per Pssbeats per minute minute The probabity is (Round to four decimal places as needed.) 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 65 and 89 beats per minute from part (b)? Why? O A. Part (b), because the cutoff values should be based on the mean pulse rate of the sample rather than individual patients OB. Part (a), because the cutoff values should be based on individual patients rather than the mean pulse rate of the sample OC. Part (b), because the cutoff values should be based on individual patients rather than the mean pulse rate of the sample O D. Both pulse rate ranges are equally acceptable. Click to select your answer(s). O type here to search 0

Explanation / Answer

Solution :

Given that mean ? = 76.7 , standard deviation ? = 11.2

a. P1 = 50.6 , P99 = 102.8

Explanation :-

=> The 1st percentile is Z = -2.326

=> The 99th percentile is Z = 2.326

=> P1 = ? + Z*?

= 76.7 + (-2.326)*11.2

= 50.6

=> P99 = ? + Z*?

= 76.7 + (2.326)*11.2

= 102.8

b. n = 45

=> P(65 < x < 89) = P((x - ?)/(?/sqrt(n)) < Z < (x - ?)/(?/sqrt(n)))

= P((65 - 76.7)/(11.2/sqrt(45)) < Z < (89 - 76.7)/(11.2/sqrt(45)))

= P(-7.0077 < Z < 7.3670)

= 1.0000

c. Option B. 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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