Question

1.

A) A population of values has a normal distribution with μ=8.2μ=8.2 and σ=55.6σ=55.6. You intend to draw a random sample of size n=249n=249.

Find the probability that a sample of size n=249n=249 is randomly selected with a mean less than 16.3.
P(M < 16.3) = ?

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

B) A population of values has a normal distribution with μ=23.7μ=23.7 and σ=83.2σ=83.2. You intend to draw a random sample of size n=156n=156.

Find the probability that a sample of size n=156n=156 is randomly selected with a mean between 14.4 and 43.7.
P(14.4 < M < 43.7) = ?

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

C) A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 139.9-cm and a standard deviation of 2.2-cm. For shipment, 21 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is greater than 139.8-cm.
P(M > 139.8-cm) = ?

Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

D)A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 126.6-cm and a standard deviation of 0.8-cm. For shipment, 12 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is between 126.5-cm and 126.8-cm.
P(126.5-cm < M < 126.8-cm) =

Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

E)
The population of weights for men attending a local health club is normally distributed with a mean of 167-lbs and a standard deviation of 28-lbs. An elevator in the health club is limited to 33 occupants, but it will be overloaded if the total weight is in excess of 6006-lbs.

Assume that there are 33 men in the elevator. What is the average weight beyond which the elevator would be considered overloaded?
average weight =  lbs

What is the probability that one randomly selected male health club member will exceed this weight?
P(one man exceeds) =
(Report answer accurate to 4 decimal places.)

If we assume that 33 male occupants in the elevator are the result of a random selection, find the probability that the evelator will be overloaded?
P(elevator overloaded) =
(Report answer accurate to 4 decimal places.)

If the evelator is full (on average) 9 times a day, how many times will the evelator be overloaded in one (non-leap) year?
number of times overloaded =
(Report answer rounded to the nearest whole number.)

F)The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.1 years and a standard deviation of 0.4 years. He then randomly selects records on 53 laptops sold in the past and finds that the mean replacement time is 3 years.

Assuming that the laptop replacement times have a mean of 3.1 years and a standard deviation of 0.4 years, find the probability that 53 randomly selected laptops will have a mean replacement time of 3 years or less.
P(M < 3 years) = ?
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Based on the result above, does it appear that the computer store has been given laptops of lower than average quality?

Answer 1