Question

1) Let x have a normal distribution with m = 10 and s = 3. Find the probability that an x value selected at random from this distribution is between 9 and 11.

In symbols, find P (9 £ x £ 11).

2) Suppose you take a sample of 33 high-school students, and measure their IQ. Assuming that IQ is normally distributed with m = 100 and s = 15, what is the probability that your sample’s IQ will be 105 or greater?

Answer 1

1)

Given

Mean = m = 10

Standard deviation = s = 3

Now

  

  

   ( from Z-table )

= 0.2586

Therefore, the probability that an x value selected at random from this distribution is between 9 and 11 is 0.2586

2.

Given

n = 33

mean = m = 100

standard deviation = s = 15

Now

  ( from Z-table )

= 0.3707

Therefore, the probability that your sample’s IQ will be 105 or greater is 0.3707