1) Suppose x has a distribution with a mean of 40 and a standard deviation of 27. Random samples of size n = 36

are drawn.

(a) Describe the x distribution

and compute the mean and standard deviation of the distribution.

x has a normal a Poisson a geometric an unknown an approximately normal a binomial

distribution with mean _x =____

and standard deviation _x =____ .

(b) Find the z value corresponding to x = 49.

z = ______

(c) Find P(x < 49).

(Round your answer to four decimal places.)

P(x < 49) = ___________

(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 49? Explain.

Yes, it would be unusual because more than 5% of all such samples have means less than 49.

No, it would not be unusual because less than 5% of all such samples have means less than 49.

Yes, it would be unusual because less than 5% of all such samples have means less than 49.

No, it would not be unusual because more than 5% of all such samples have means less than 49.

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2) Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 74 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean = 74 tons and standard deviation = 1.1 ton.

(a) What is the probability that one car chosen at random will have less than 73.5 tons of coal? (Round your answer to four decimal places.)

_________________________

(b) What is the probability that 33 cars chosen at random will have a mean load weight x of less than 73.5 tons of coal? (Round your answer to four decimal places.)

____________________

(c) Suppose the weight of coal in one car was less than 73.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment?

Yes

No

Suppose the weight of coal in 33 cars selected at random had an average x of less than 73.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why?

Yes, the probability that this deviation is random is very small.

Yes, the probability that this deviation is random is very large.

No, the probability that this deviation is random is very small.

No, the probability that this deviation is random is very large.

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3) Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean = 6150 and estimated standard deviation = 1550. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)

___________________

(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?

The probability distribution of x is not normal.

The probability distribution of x is approximately normal with _x = 6150 and _x = 1096.02.

The probability distribution of x is approximately normal with _x = 6150 and _x = 775.00.

The probability distribution of x is approximately normal with _x = 6150 and _x = 1550.

What is the probability of x < 3500? (Round your answer to four decimal places.)

_____________________

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

__________________

(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?

The probabilities stayed the same as n increased.

The probabilities increased as n increased.

The probabilities decreased as n increased.

If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.