Question

Assume that adults have IQ scores that are normally distributed, with a mean of 102 and a standard deviation of 16. Find the probability that a randomly selected individual has an IQ between 81 and 109. Choose the correct value:

Choose one:

a) 0.5647

b) 0.5749

c) 0.5747

d) 0.5649

Answer 1

Given that adults have IQ scores that are normally distributed, with a mean of = 102 and a standard deviation of = 16.

Since the distribution is normal hence Z statistic is applicable for probability calculation.

thus P( 81 <X < 109) is calculated by finding the Z score at X = 81, 109 as:

Now teh probability is computed as P( -1.3125 < Z < 0.4375), hence the probability is computed using the excel formula for normal distribution which is =NORM.S.DIST(0.44, TRUE) - NORM.S.DIST(-1.31, TRUE), now the probability is computed as:

= 0.6700 - 0.0951

b) 0.5749

NOTE : The probability value may be calculated as 0.5747 is the Z score is rounded upto 3 decimals, hence please follow accordingly, feel free to ask if query remains.

The Z table uses the Z score upto 2 decimal hence the values are denoted in Z table as: