The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
a) What is the probability that a randomly person has an IQ between 85 and 115?
b) Find the 90th percentile of the IQ distribution
c) If a random sample of 100 people is selected, what is the standard deviation of the sample mean?
a) 68% from the empirical rule calculator
b) P(z) = 0.90. so z = 1.28152 using Excel NORMSINV(0.9)<br />
(X - 100)/10 = 1.21852
X = 113 rounded up
c) Sample standard deviation is the population standard deviation divided by the square root of the sample size
15/sqrt(100) = 15/10 = 1.5
a) What is the probability that a randomly person has an IQ between 85 and 115?
b) Find the 90th percentile of the IQ distribution
c) If a random sample of 100 people is selected, what is the standard deviation of the sample mean?
a) 68% from the empirical rule calculator
b) P(z) = 0.90. so z = 1.28152 using Excel NORMSINV(0.9)<br />
(X - 100)/10 = 1.21852
X = 113 rounded up
c) Sample standard deviation is the population standard deviation divided by the square root of the sample size
15/sqrt(100) = 15/10 = 1.5