- At a large publishing company, the mean age of proofreaders is 36.2 years, and the standard deviation is 3.7 years. Assume the variables are normally distributed.
a. If a proofreader in the company is randomly selected, find the probability that his or her age will be between 36 and 37.5 years
Attempt (unverified): Probability distribution of right-hand side of the mean on the bell curve:
35% of 1 Standard Deviation = 1.295 years
36.2+1.295 = 37.495 (approx. 37.5 years)
Therefore, 35% of 34% (half of one standard deviation on the right) = 11.9%
We do the same thing for the left-hand side and end up with: 6.25% of 34% (half of 1s to the left) = 2.125% [gives us 35.97 years =~ 36 years]
Therefore, P(age between 36 and 37.5 years) = 11.9 + 2.125 = 14.025% (final answer)
b. If a random sample of 15 proofreaders is selected, find the probability that the mean age of the proofreaders in the sample will be between 36 years and 37.5 years.
P(age between 36 and 37.5) = 14.025% [from A]
n = 15
-=HOW DO I PROCEED FROM HERE=- ?
PLEASE ASSIST. Thank you.