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 = 190 and a standard deviation σ = 15.

(a) Use Chebyshev's Rule to make a statement about the minimum percentage of colleges that have between 145 and 235 teachers. (Round your answer to two decimal places if necessary.)
Correct Answer: 88.9

(b) Assume that the population is mound-shaped symmetrical. What proportion of colleges have less than 205 teachers?

I need help with letter B please. Thank you in advance :)

Answer 1

Solutionb:

P(X<205)

since its symmetrical distribution is normal

mean=190

sd=15

z=x-mean/sd

z=205-190/15

z=1

P(Z<1)

from standard normal distribution

P(Z<1)=0.8413

ANSWER:0.8413