Question

Consider a population consisting of the number of teachers per college at small 2-year colleges. Suppose that the number of teachers per college has an average μ = 150 and a standard deviation σ = 20.

a. Use Chebyshev's Rule to make a statement about the minimum percentage of colleges that have between 90 and 210 teachers. (Round your answer to two decimal places if necessary.)

(b) Assume that the population is mound-shaped symmetrical. What proportion of colleges have less than 170 teachers?

Answer 1

a)
`(8)/(9)` =0.89

b) 0.8413

Explanation:

we know that

`P(║ x -\mu║ \leq  k\sigma) \geq 1 -(1)/(k^2)`

`so, \mu = 150, \sigma = 20`

`k =  (210 - 150)/(20) =(150 - 90)/(20) = 3`

`P(║ x -150 ║ \leq  3* 20) \geq 1 -(1)/(3^2) = (8)/(9)`

x - N(150, 20^2)

`P(X \leq 170) = 0.8413447`

check

`P norm = (170 - 150)/(20)= 0.8413447`