Sam is a night watchman in a large warehouse. During one complete round of the warehouse, he must check in at 40 different checkpoints, all of which are about the same distance apart. At each checkpoint, he inserts a key that tells a central computer the time he checked in. Let x be a random variable representing the length of time from one check-in to the next. While monitoring Sam's check-in times for the past year, the computer found the mean of the x distribution be mean=6.2 minutes with standard deviation=1.7 minutes.

1. Refer to the data above regarding check-in time intervals.

In one complete round of the warehouse, there are 40 check-in time intervals. What is the probability that the average check-in time interval will be from 6 to 7 minutes?

a. 0.8531 b. 0.7689 c. 0.2704 d. 0.9837 e. 0.4985

2. Refer to the data above regarding check-in time intervals.

In two complete rounds of the warehouse, there are 80 check-in time intervals. What is the probability that the average check-in time interval will be from 6 to 7 minutes?

a. 0.8531 b. 0.7689 c. 0.2704 d. 0.9837 e. 0.4985

The taxi and takeoff time for commercial jets is a random variable x with a mean of 8 minutes and a standard deviation of 3 minutes. Assume that the distribution of taxi and takeoff time is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and they take off one at a time on a given runway.

1. Refer to the data above regarding taxi and takeoff times.

What is the probability that for 36 jets on a given runway total taxi and takeoff time will be less than 300 minutes? That is, the average will be less than 300/36=8.33 minutes per plane.

a. 0.1587 b. 0.3669 c. 0.6331 d. 0.7454 e. 0.8413

2. Refer to the data above regarding taxi and takeoff times.

What is the probability that for 36 jets on a given runway total taxi and takeoff time will be less than 270 minutes? That is, the average will be more than 270/36=7.5 minutes per plane.

a. 0.1587 b. 0.3669 c. 0.6331 d. 0.7454 e. 0.8413