Question

. IQ's are normally distributed with a mean of 100 and a standard deviation of 10. If a person is selected at random, what is the probability that his/her IQ is between 100 and 115? What is the probability that his/her IQ is higher than 120? What about lower than 100?

Answer 1

Solution :

Given that ,

mean = = 100

standard deviation = = 10

P(100 < x < 115) = P((100 - 100)/ 10) < (x - ) / < (115 - 100) / 10) )

= P(0 < z < 1.5)

= P(z < 1.5) - P(z < 0)

= 0.9332 - 0.5

= 0.4332

Probability = 0.4332

P(x > 120) = 1 - P(x < 120)

= 1 - P((x - ) / < (120 - 100) / 10)

= 1 - P(z < 2)

= 1 - 0.9772   

= 0.0228

Probability = 0.0228

P(x < 100) = P[(x - ) / < (100 - 100) / 10]

= P(z < 0)

= 0.5

about = 0.5