For a certain population IQ-scores are approximately normally distributed with a mean of 97 points and a standard deviation of 16 points. (a) What is the z-score for a member of this population that has an IQ of 141? (Give your answer to two decimal places.)

(b) What is the probability that a person chosen at random from this group has an IQ in excess of 141? (Give your answer to two decimal places.)

(c) What IQ-score is at the 95th percentile? (Give your answer to two decimal places.)

(d) Find the median, quartiles and interquartile range for these IQ scores. (Give your answers to two decimal places.)
Median =
Q1 =
Q3 =
IQR =

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

inch

step-by-step explanation:

yard and mile are too big.