Question

Question 2: (Marks: 2)

Intelligence quotients (IQs) on the Stanford-Binet intelligence test are normally distributed with a mean of 100 and a standard deviation of 16. In Exercises a–d, use the 68–95–99.7 Rule to find the percentage of people with IQs

1. between 84 and 116

2. between 84 and 100

3. above 132

4. below 68

Answer 1

2)

Solution :

Given that,

Using Empirical rule,

P( - 1< X < + 1) = 68%

P( - 2< X < + 2) = 95%

P( - 3< X < + 3) = 99.7%

(a)

P( - 1< X < + 1) = 68%

P(100 - 16 < X < 100 + 16) = 68%

P(84 < X < 116) = 68%

68%

(b)

P(84 < X < 100) = P(X < 100) - P(X < 84) = 0.5 - 0.16 = 34%

(c)

P(X > 132) = P=1 - P(X < 132) = 1 - 0.975 = 2.5%

(d)

P(X < 68) = 2.5%