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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