Finding the probability that a randomly selected adult has an IQ less than 132...

Question

Assume that adults have IQ scores that are normally distributed with a mean of 105 and a standard deviation of 15 . Find the probability that a randomly selected adult has an IQ less than 132. Click to view page 1 of the table.LOADING... Click to view page 2 of the table.LOADING... The probability that a randomly selected adult has an IQ less than 132 is ?

​(Type an integer or decimal rounded to four decimal places as​ needed.)

Answer 1

calculate the z score = (x - mean)/sd = (132=105)/15 = 27/15 = 9/5 = 18/10 = 1.8 which is close to 2, but a little less. An online z table calculator shows Pr(<z)= 0.96407 when z=1.8

had z been 2, 90% of the adults would have been between -2 and 2 standard deviations. But -1.8 and 1.8 standard deviations is a little less than 90%

the other 10% would be divided as 5% above 132 and 5% below 105-27= 78.

For z=2, P(<z) = 0.95, for z=1.8 P(<z) = 0.96407