# 4.Suppose x has a distribution with a mean of and a standard deviation of .

4.Suppose x has a distribution with a mean of and a standard deviation of . Random samples of size n =

901264 are drawn.

(a) Describe the X distribution.

x has a geometric distribution.

x has a binomial distribution.

x has a normal distribution.

x has an unknown distribution.

x has an approximately normal distribution.

x has a Poisson distribution.

Compute the mean and standard deviation of the distribution. (For each answer, enter a number.)

mu sub x bar =

sigma sub x bar =

(b) Find the z value corresponding to x = 87. (Enter an exact number.)

z =

(c) Find P(x < 87). (Enter a number. Round your answer to four decimal places.)

P(x bar < 87)=

(d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 87? Explain.

Yes, it would be unusual because more than 5% of all such samples have means less than 87.

No, it would not be unusual because less than 5% of all such samples have means less than 87.

Yes, it would be unusual because less than 5% of all such samples have means less than 87.

No, it would not be unusual because more than 5% of all such samples have means less than 87.

5.

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

μ = 8; σ = 6

P(5 ≤ x ≤ 14) =

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