Mean standard deviation and required probability for the given probability distribution.
What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? 25466 nurses in Great Britain, furthermore Nightingale made a strict distinction between nurses and domestic servants.
|
Age range (Yr)
|
20-29
|
30-39
|
40-49
|
50-59
|
60-69
|
70-79
|
80+
|
|
Mid point x
|
24.5
|
34.5
|
44.5
|
54.5
|
64.5
|
74.5
|
84.5
|
|
Percent of nurses
|
5.7%
|
9.7%
|
19.5%
|
29.2%
|
25.0%
|
9.1%
|
1.8%
|
a. Using age midpoints x and the percentages of nurses, do we have a valid probability distribution? Give details.
b. Use a histogram to graph the probability distribution of part(a).
c. Find the probability that the British nurse selected at random in 1851 will be 60 years of age or older.
d. calculate the expected age µ of a British nurse contemporary to Florence Nightingale.
e. work out the standard deviation σ for the age of nurses shown in the distribution.