Question

A normal random variable x has mean ? = 1.6 and standard deviation ? = 0.17. Find the probability associated with each of the following intervals. (Round your answers to four decimal places.)

(a)    

1.00 < x < 1.30

(b)    

x > 1.32

(c)    

1.25 < x < 1.50

Answer 1

Solution :

Given that ,

mean = = 1.6

standard deviation = = 0.17

(a)

P(1 < x < 1.30) = P((1 - 1.6 / 0.17) < (x - ) / < (1.30 - 1.6) / 0.17) )

P(1 < x < 1.30) = P(-3.53 < z < -1.76)

P(1 < x < 1.30) = P(z < -1.76) - P(z < -3.53)

P(1 < x < 1.30) = 0.0392 - 0.0002 = 0.0390

Probability = 0.0390

(b)

P(x > 1.32) = 1 - P(x < 1.32)

= 1 - P((x - ) / < (1.32 - 1.6) / 0.17)

= 1 - P(z < -1.647)

= 1 - 0.0498

= 0.9502

P(x > 1.32) = 0.9502

Probability = 0.9502

(c)

P(1.25 < x < 1.50) = P((1.25 - 1.6 / 0.17) < (x - ) / < (1.50 - 1.6) / 0.17) )

P(1.25 < x < 1.50) = P(-2.059 < z < -0.588)

P(1.25 < x < 1.50) = P(z < -0.588) - P(z < -2.059)

P(1.25 < x < 1.50) = = 0.2783 - 0.0197 = 0.2586

Probability = 0.2586