Question

The following table shows the approximate numbers of school goers in the United States (residents who attended some educational institution) in 1998, broken down by age group. Age 3−6.9 7−12.9 13−16.9 17−22.9 23−26.9 27−42.9 Population (millions) 8 22 15 13 3 5 Use the rounded midpoints of the given measurement classes to compute the probability P distribution of the age X of a school goer. (Round probabilities to four decimal places.)

Age 5 10 15 20 25 35 P(X = x) Compute the expected value of X, E(X). (Round your answer to one decimal place.)

E(X) = What information does the expected value give about residents enrolled in schools? (Round your answer to one decimal place.) In 1998, was years old.

Answer 1

(a) From the given data, the probability P distribution of the age X of a school goes is calculated as follows:

Class Interval	Mid Point (x)	Probability (p)
3 - 6.9	5	8/66 = 0.1212
7 - 12.9	10	22/66 =0.3333
13- 16.9	15	15/66 = 0.2273
17 - 22.9	20	13/66 = 0.1970
23 - 26.9	25	3/66 = 0.0455
27 - 42.9	35	5/66= 0.0758

So,

the probability P distribution of the age X of a school goes is given by:

(a) From the given data, the probability P distribution of the age X of a school goes is calculated as follows:

Age (x)	Probability (p)
5	0.1212
10	0.3333
15	0.2273
20	0.1970
25	0.0455
35	0.0758

(b)

The Expected Value of X, E(X) is calculated as follows:

Age (x)	Probability (p)	xp
5	0.1212	0.6060
10	0.3333	3.3330
15	0.2273	3.4095
20	0.1970	3.9400
25	0.0455	1.1375
35	0.0758	2.6530
E(X) =		15.0790

So

The Expected Value of X, E(X) = 15.1

In 1998, the average number of school goes in the United Stales was 15.1 millions