Question

Exercise 11

A normal distributed population of measurements has a population mean of 140 and a standard deviation of 8.

• What is the probability that a measurement taken at random in the population will be less than 160?

• What is the probability that a measurement taken at random in the population will be greater than 150?

• What is the probability that a measurement taken at random in the population will be between 150 and 160?

Answer 1

11)

Solution :

Given that ,

mean = = 140

standard deviation = = 8

(a)

P(x < 160) = P((x - ) / < (160 - 140) / 8)

= P(z < 2.5)

Using standard normal table,

P(x < 160) = 0.9938

Probability = 0.9938

(b)

P(x > 150) = 1 - P(x < 150)

= 1 - P((x - ) / < (150 - 140) / 8)

= 1 - P(z < 1.25)

= 1 - 0.8944   

= 0.1056

P(x > 150) = 0.1056

Probability = 0.1056

(c)

P(150 < x < 160) = P((150 - 140) / 8) < (x - ) / < (160 - 140) / 8) )

= P(1.25 < z < 2.5)

= P(z < 2.5) - P(z < 1.25)

= 0.9938 - 0.8944

Probability = 0.0994