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. Age range (yr) Midpoint x Percent of nurses 20-29 24.5 40-49 50-59 54.5 29.7% 30-39 60-69 70-79 80+ 34.5 44.5 64.5 74.5 9.0% 84.5 5.2% 9.4% 19.9% 25.0% 1.8% (a) Using the age midpoints x and the percent of nurses, do we have a valid probability distribution? Explain. O No. The events are indistinct and the probabilities do not sum to 1. O No. The events are indistinct and the probabilities sum to 1. O Yes. The events are distinct and the probabilities sum to 1. O Yes. The events are distinct and the probabilities do not sum to 1. (b) Use a histogram to graph the probability distribution in part (a). 30 30 25 25 20 20 K of Nurses 15 % of Nurses 15 10 10 0T 24.5 34.5 44.5 54.5 64.5 745 84.5 24.5 34.5 44.5 54.5 64.5 745 84.5 Age Age 30 30 25 25 20 20 % of Nurses 15- % of Nurses 15 10 10 24.5 34.5 44.5 54.5 64.5 745 84.5 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Age Age (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 u of a British nurse contemporary to Florence Nightingale. (Round your answer to two decimal places.) yr (e) Compute the standard deviation o for ages of nurses shown in the distribution. (Round your answer to two decimal places.) yr

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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.
Age range (yr)
Midpoint x
Percent of nurses
20-29
24.5
40-49
50-59
54.5
29.7%
30-39
60-69
70-79
80+
34.5
44.5
64.5
74.5
9.0%
84.5
5.2%
9.4%
19.9%
25.0%
1.8%
(a) Using the age midpoints x and the percent of nurses, do we have a valid probability distribution? Explain.
O No. The events are indistinct and the probabilities do not sum to 1.
O No. The events are indistinct and the probabilities sum to 1.
O Yes. The events are distinct and the probabilities sum to 1.
O Yes. The events are distinct and the probabilities do not sum to 1.
(b) Use a histogram to graph the probability distribution in part (a).
30
30
25
25
20
20
K of Nurses 15
% of Nurses 15
10
10
0T
24.5 34.5 44.5 54.5 64.5 745 84.5
24.5 34.5 44.5 54.5 64.5 745 84.5
Age
Age
30
30
25
25
20
20
% of Nurses 15-
% of Nurses 15
10
10
24.5 34.5 44.5 54.5 64.5 745 84.5
24.5 34.5 44.5 54.5 64.5 74.5 84.5
Age
Age
(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 u of a British nurse contemporary to Florence Nightingale. (Round your answer to two decimal places.)
yr
(e) Compute the standard deviation o for ages of nurses shown in the distribution. (Round your answer to two decimal places.)
yr
Transcribed Image Text: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. Age range (yr) Midpoint x Percent of nurses 20-29 24.5 40-49 50-59 54.5 29.7% 30-39 60-69 70-79 80+ 34.5 44.5 64.5 74.5 9.0% 84.5 5.2% 9.4% 19.9% 25.0% 1.8% (a) Using the age midpoints x and the percent of nurses, do we have a valid probability distribution? Explain. O No. The events are indistinct and the probabilities do not sum to 1. O No. The events are indistinct and the probabilities sum to 1. O Yes. The events are distinct and the probabilities sum to 1. O Yes. The events are distinct and the probabilities do not sum to 1. (b) Use a histogram to graph the probability distribution in part (a). 30 30 25 25 20 20 K of Nurses 15 % of Nurses 15 10 10 0T 24.5 34.5 44.5 54.5 64.5 745 84.5 24.5 34.5 44.5 54.5 64.5 745 84.5 Age Age 30 30 25 25 20 20 % of Nurses 15- % of Nurses 15 10 10 24.5 34.5 44.5 54.5 64.5 745 84.5 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Age Age (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 u of a British nurse contemporary to Florence Nightingale. (Round your answer to two decimal places.) yr (e) Compute the standard deviation o for ages of nurses shown in the distribution. (Round your answer to two decimal places.) yr
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