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

Answer:

a) $\frac{8}{9}$ =0.89

b) 0.8413

Step-by-step explanation:

we know that

$P(║ x -\mu║ \leq k\sigma) \geq 1 -\frac{1}{k^2}$

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

$k = \frac{210 - 150}{20} =\frac{150 - 90}{20} = 3$

$P(║ x -150 ║ \leq 3\times 20) \geq 1 -\frac{1}{3^2} = \frac{8}{9}$

x - N(150, 20^2)

$P(X \leq 170) = 0.8413447$

check

$P norm = \frac{170 - 150}{20}= 0.8413447$