Question

The times per week a student uses a lab computer are normally​ distributed, with a mean of 6.1 hours and a standard deviation of 1.3 hours. A student is randomly selected. Find the following probabilities.

​(a) Find the probability that the student uses a lab computer less than 4 hours per week.

​(b) Find the probability that the student uses a lab computer between 7 and 8 hours per week.

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

Answer 1

Given,

= 6.1

= 1.3

a) find p(x< 4)

We know that z=(x-​​​​​​) /

p(x < 4) = 0.5 - p(z < 4-6.1/1.3)

= 0.5 - p(z < -1.62)

= 0.5 - 0.4474

p(x < 4) = 0.0526

Therefore probability that student uses computer lab less than 4 is 0.0526.

2) p(7 < x < 8) = p(z < 8-6.1/1.3) - p(z < 7-6.1/1.3)

= p(z < 1.46) - p(z < 0.69)

= 0.4279 - 0.2549

p(7 < x < 8) = 0.173

Therefore probability that student uses computer lab in between 7 and 8 is 0.2156.

3) p(x > 9)

p(x > 9) = 0.5 - p(z < 9-6.1/1.3)

= 0.5 - p(z < 2.23)

= 0.5 - 0.4871

p(x > 9) = 0.0129

Therefore the probability that the student uses computer lab is more than 9 hours is 0.0129.