Using the age midpoints x and the percentage of nurses, do we have a valid probability distribution? Explain Use a histogram to graph the probability distribution of part (a). Compute the expected age (mean) of a nurse. Compute the standard deviation for ages of nurses. What is the probability that a British nurse selected at random was younger than 60?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2AGP
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  1. What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? 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%

 

  1. Using the age midpoints x and the percentage of nurses, do we have a valid probability distribution? Explain
  2. Use a histogram to graph the probability distribution of part (a).
  3. Compute the expected age (mean) of a nurse.
  4. Compute the standard deviation for ages of nurses.
  5. What is the probability that a British nurse selected at random was younger than 60?
Expert Solution
Working
x p(x) xp(x) (x-xbar)^2 (x-xbar)^2p(x)
24.5 0.057 1.3965 856.1476 48.80041
34.5 0.097 3.3465 370.9476 35.98192
44.5 0.195 8.6775 85.7476 16.72078
54.5 0.292 15.914 0.5476 0.159899
64.5 0.25 16.125 115.3476 28.8369
74.5 0.091 6.7795 430.1476 39.14343
84.5 0.018 1.521 944.9476 17.00906
    53.76   186.6524
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