Question

Movie length. Children’s movies run an average of 98 minutes with a standard deviation of 10 minutes. You check out a movie, selected at random without reading the running time on the box, from the library to entertain your kids so you can study for your probability test. Assume that your kids will be occupied for the entire length of the movie.

a. What is the probability that your kids will be occupied for at least the 2 hours you would like to study?

b. What is range for the bottom quartile (lowest 25%) of time they will be occupied?

c. What are the limits for the central 95% of times your kids will be occupied?

Answer 1

Given,

= 98 , = 10

We convert this to standard normal as

P( X < x) = P( Z < x - / )

a)

P( X >= 120) = P( Z > 120 - 98 / 10)

= P( Z > 2.2)

= 0.0139

b)

Lower quartile = + Z , Where Z is critical value at 25% confidence level.

= 98 - 0.6745 * 10

= 91.255

c)

Limits for middle 95% confidence level,

Z

98 1.96 * 10

That is

98 - 1.96 * 10 and 98 + 1.96 * 10

78.4 and 117.6