Question

Items 4 through 5 refer to the following:

Assume a normal random variable, X, with mean 90 and standard deviation 10. Find the probability that a randomly chosen value of X is less than 95.

a. 0.5793 b. 0.5987 c. 0.2057 d. 0.6915 e. 0.7734

Find the probability that a randomly chosen value of X is between 60 and 100.

a. 0.6827 b. 0.6247 c. 0.5404 d. 0.4772 e. 0.8400

Answer 1

Solution :

Given that ,

mean = = 90

standard deviation = = 10

(a)

P(x < 95) = P[(x - ) / < (95 - 90) / 10]

= P(z < 0.5)

= 0.6915

Probability = 0.6915

(b)

P(60 < x < 100) = P[(60 - 90)/ 10) < (x - ) /  < (100 - 90) / 10) ]

= P(-3 < z < 1)

= P(z < 1) - P(z < -3)

= 0.8413 - 0.0013

= 0.8400

Probability = 0.8400