Question

2. What was the age distribution of nurses in Great Britain at the time of Florence Nightingaler We have the following data from Florence Nightingale's writing 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 Percantage of Nurses 5.7% 9.7% 19.5% 29.2% 25.0% 9.1% 1.8% A. Using the age midpoints x and the percentage of nurses, do we have a valid probability distribution? Explain B. Use a histogram to graph the probability distribution of part (a). C. Compute the expected age (mean) of a nurse. D. Compute the standard deviation for ages of nurses. E. What is the probability that a British nurse selected at random was younger than 60?

Answer 1

P(x) L aPcx) X²PCM) 24.5 134.5 44.5 154.5 0.057 0.097 0. 195 0.292 0.25 o.og 0.018 1.3965 3.3465 8.6775 15.914 16.125 6.7795 21.521 34.21425 115.45425 886.14875 867.313 1040.0625 505.07275 128.5245 64.5 174.5 84.5 sum = I 1 I 53.76 I 3076.79. distribution 1 Yes this is valid probability since in tu , OLP(1) LI 1) E part-1 0.31 6 6 24.5 34.5 44.5 sur 64.5 74.5 84.5 t

- @ expected age = E = Expca) = 53.76 years ✓ Variance = { x² pcx) - [End]² bit = 8076.79 - 153.70) = 108.6524 standard deviation = 108.6524 = 13.66 years N prob ( a 2 60 = 0.057 +0.097 + 0.195 + 0.292 = 0.641 /