Question

Q1) Give the R code for the following problems

a) Suppose IQ is normally distributed with a mean of 100 and a standard deviation of 15. Give the R code needed to find the IQ that separates the top 5% from the others.

b) Suppose IQ is normally distributed with a mean of 100 and a standard deviation of 15. Give the R code needed to find the IQ that corresponds to the 75% percentile.

c) Suppose IQ is normally distributed with a mean of 100 and a standard deviation of 15. Give the R code needed to find the probability a randomly selected person has an IQ less than 80.

Answer 1

Solution:

Given that,

mean = =100

standard deviation = = 15

Using standard normal table,

a ) P( Z > z) = 5%

P(Z > z) = 0.05

1 - P( Z < z) = 0.05

P(Z < z) = 1 - 0..05

P(Z < z) = 0.95

z = 1.64

Using z-score formula,

x = z * +

x = 1.64 * 15 + 100

x = 124.6

b ) P(Z < z) =75%

P(Z < z) = 0.75

z = 0.67

Using z-score formula,

x = z * +

x = 0.67 * 15 + 100

x =110.05

c ) P( x < 80 )

P ( x - / ) < ( 80 - 100 / 15)

P ( z < - 20 / 15 )

P ( z < -1.33)

= 0.0918

Probability = 0.0918