SOLUTION: The mean age of new professors of an organization is 40 with a standard deviation of 6 . Between which two age limit must 75% of the professors lie? a) [28, 52] b) [30, 50] c

Algebra ->  Probability-and-statistics -> SOLUTION: The mean age of new professors of an organization is 40 with a standard deviation of 6 . Between which two age limit must 75% of the professors lie? a) [28, 52] b) [30, 50] c      Log On


   



Question 1042965: The mean age of new professors of an organization is 40 with a standard deviation of 6 . Between which two age limit must 75% of the professors lie?
a) [28, 52]
b) [30, 50]
c) [34, 46]
d) None of these

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Apply Chebyshev's Theorem P%28abs%28X+-+mu%29+%3C=+k%2Asigma%29+%3E=+1-1%2Fk%5E2,
with mu+=+40 and sigma+=+6.
Now let k = 2.
This will yield P%28abs%28X+-+40%29+%3C=+12%29+%3E=+3%2F4+=+0.75.
===> P%2828+%3C=+X+%3C=+52%29+%3E=+0.75.
Therefore the answer is a) [28, 52].