Part 1

A company produces steel rods. The lengths of the steel rods arenormally distributed with a mean of 198.9-cm and a standarddeviation of 2.3-cm. For shipment, 22 steel rods are bundledtogether.

Find P₅₂, which is the average lengthseparating the smallest 52% bundles from the largest 48%bundles.
P₅₂ = _____ cm

Part 2

Scores for a common standardized college aptitude test arenormally distributed with a mean of 513 and a standard deviation of96. Randomly selected men are given a Test Prepartion Course beforetaking this test. Assume, for sake of argument, that the test hasno effect.

If 1 of the men is randomly selected, find the probability that hisscore is at least 616.
P(X > 616) = __________

If 5 of the men are randomly selected, find the probability thattheir mean score is at least 616.
P(M > 616) = __________

Part 3

A population of values has a normal distribution with ?=152.8and ?=59.7. You intend to draw a random sample of size n=211.

Find the probability that a single randomly selected value isbetween 140.9 and 164.3.
P(140.9 < X < 164.3) = __________

Find the probability that a sample of size n=211 is randomlyselected with a mean between 140.9 and 164.3.
P(140.9 < M < 164.3) = _____________

Part 4

A population of values has a normal distribution with ?=164.8and ?=37.2. You intend to draw a random sample of size n=108.

Find the probability that a sample of size n=108 is randomlyselected with a mean between 154.1 and 169.8.
P(154.1 < M < 169.8) = _________

Part 5

A population of values has a normal distribution with ?=143.9and ?=89.6. You intend to draw a random sample of size n=217.

Find the probability that a single randomly selected value isbetween 133 and 162.1.
P(133 < X < 162.1) = ________

Find the probability that a sample of size n=217 is randomlyselected with a mean between 133 and 162.1.
P(133 < M < 162.1) = _______________

Part 6

A population of values has a normal distribution with ?=179 and?=98.2. You intend to draw a random sample of size n=75.

Find the probability that a sample of size n=75 is randomlyselected with a mean less than 181.3.
P(M < 181.3) = ___________