What was the age distribution of nurses in Great Britain at the time of Florence

Question

What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Suppose we have the following information. Note: In 1851 there were 25,466 nurses in Great Britain.

(a) Using the age midpoints x and the percent of nurses, do we have a valid probability distribution? Explain.

Yes. The events are distinct and the probabilities sum to 1.No. The events are indistinct and the probabilities sum to 1.    Yes. The events are distinct and the probabilities do not sum to 1.No. The events are indistinct and the probabilities do not sum to 1.

(b) Use a histogram to graph the probability distribution in part (a).

(c) Find the probability that a British nurse selected at random in 1851 would be 60 years of age or older. (Round your answer to three decimal places.)


(d) Compute the expected age of a British nurse contemporary to Florence Nightingale. (Round your answer to two decimal places.)
yr

(e) Compute the standard deviation for ages of nurses shown in the distribution. (Round your answer to two decimal places.)
yr

Age range (yr) 20-29 30-39 40-49 50-59 60-69 70-79 80+ Midpoint x 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of nurses 5.3% 9.1% 19.5% 29.4% 24.6% 10.5% 1.6% 20 % of Nurses 15- 24.5 34.5 44.5 54.5 64.5 745 84.5 Age

Explanation / Answer

a)Yes. The events are distinct and the probabilities sum to 1.

b) top left histogram

c) probability that a British nurse selected at random in 1851 would be 60 years of age or older. =0.246+0.105+0.016=0.367

d)

expected age =54.18

e)standard deviation =13.58

x p(x) xP(x) (x-)2 (x-)2P(x) 24.5 0.053 1.299 880.902 46.688 34.5 0.091 3.140 387.302 35.245 44.5 0.195 8.678 93.702 18.272 54.5 0.294 16.023 0.102 0.030 64.5 0.246 15.867 106.502 26.200 74.5 0.105 7.823 412.902 43.355 84.5 0.016 1.352 919.302 14.709 total 1 = 54.18 2800.717 2= 184.4976 std deviation=     =    2 = 13.5830

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