Question

IQ scores are normally distributed with a mean of 100 and a standard deviation of 16.
a) What percent of people have an IQ of less than 68?
b) What percent of people have an IQ between 100 and 132?
c) Write a 68% confidence interval.
d) If 10,000 people are studied, how many will score above a 148 on the IQ?

Answer 1

Answer:

Given

• μ = 100
• σ = 16

a)

x = 68

• z = (x - μ)/σ =
• (68 - 100)/16 = -2
• z-score = 0.0228 = 2.28%

b)

x = 100 and x = 132

• z = (100 - 100)/16 = 0, z-score = 50%
• z = (132 - 100)/16 = 2, z-score = 0.9772 = 97.72%
• 97.72% - 50% = 47.72%

c)

68% confidence interval, assumed sample number n = 100

z-score representing 68% = 0.47

• CI = μ ± z× σ/√n
• CI = 100 ± 0.47*16/√100 =
•     = 100 ± 0.752

d)

• n = 10000
• x = 148
• z = (148 - 100)/16 = 3, z-score is 0.9987  

Number of people scored above 148:

• (1 - 0.9987)*10000 = 13 people