Question

The following table shows the approximate number of males of Hispanic origin employed in the United States in a certain year, broken down by age group.

Age	15-24.9	25-54.9	55-64.9
Employment (thousands)	25,000	16,000	1,000

(a) Use the rounded midpoints of the given measurement classes to compute the expected value and the standard deviation of the age X of a male Hispanic worker in the United States. (Round all probabilities and intermediate calculations to two decimal places.)

expected value	yrs old
standard deviation	yr

(b) In what age interval does the empirical rule predict that 68 percent of all male Hispanic workers will fall? (Round answers to the nearest year.)

Answer 1

a)

Midpoint = (Lower limit + upper limit )/ 2

For interval, 15-24.9, midpoint = 15 + 24.9 / 2 = 19.95

For interval 25-54.9, midpoint = 25 + 54.9 / 2 = 39.95

For interval 55- 64.9 , midpoint= 55 + 64.9 / 2 = 59.95

Let X be midpoint and Employment be f

Then,

E(X) = X * f / f

= 19.95 * 25000 + 39.95 * 16000 + 59.95 * 1000 / (25000 + 16000 + 1000)

= 28.52

Standard deviation = Sqrt [ ( x²f - n * mean² ) / n -1 ] Where n = f

= Sqrt[ 19.95² * 25000 + 39.95² * 16000 + 59.95² * 10000 - 51000 * 28.52² / 50999)]

= 10.82

b)

according to emperical rule,

Approximately, 68% data falls between 1 standard deviation of the mean.

Range = (Mean - standard deviation , Mean + standard deviation)

= (28.52 - 10.82 , 28.52 + 10.82 )

= (18 , 39)