Question

The times per week a student uses a lab computer are normally​ distributed, with a mean of 6.3 hours and a standard deviation of 1.2 hours. A student is randomly selected. Find the following probabilities.

​(a) Find the probability that the student uses a lab computer less than 5 hours per week.

​(b) Find the probability that the student uses a lab computer between 6 and 8 hours per week.

​(c) Find the probability that the student uses a lab computer more than 9 hours per week.

Answer 1

Solution :

(a)

P(x < 5) = P[(x - ) / < (5 - 6.3) / 1.2]

= P(z < -1.08)

= 0.1401

probability = 0.1401

(b)

P(6 < x < 8) = P[(6 - 6.3)/ 1.2) < (x - ) /  < (8 - 6.3) / 1.2) ]

= P(-0.25 < z < 1.42)

= P(z < 1.42) - P(z < -0.25)

= 0.9222 - 0.4013

= 0.5209

Probability = 0.5209

(c)

P(x > 9) = 1 - P(x < 9)

= 1 - P[(x - ) / < (9 - 6.3) / 1.2)

= 1 - P(z < 2.25)

= 1 - 0.9878

= 0.0122

Probability = 0.0122