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.

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	5.2%	9.3%	19.2%	29.1%	24.7%	10.7%	1.8%

1. 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.)

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

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

Answer 1

1)

P(  60 years of age or older) =0.247+0.107+0.018 =0.372

2)

x	P(X=x)	xP(x)	x2P(x)
24.5	0.052	1.27400	31.21300
34.5	0.093	3.20850	110.69325
44.5	0.192	8.54400	380.20800
54.5	0.291	15.85950	864.34275
64.5	0.247	15.93150	1027.58175
74.5	0.107	7.97150	593.87675
84.5	0.018	1.52100	128.52450
total		54.3100	3136.4400
	E(x) =μ=	ΣxP(x) =	54.3100
	E(x2) =	Σx2P(x) =	3136.4400
	Var(x)=σ2 =	E(x2)-(E(x))2=	186.863900
	std deviation=	σ= √σ2 =	13.66982

from above:

  expected age μ =54.31

3)

standard deviation σ =13.67