Suppose x has a distribution with a mean of 50 and a standard deviation of 9. Random samples of size n = 36 are drawn.

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Suppose x has a distribution with a mean
of 50 and a standard deviation of 9. Random samples
of size n = 36 are drawn.
(a)
Describe the distribution.
has a binomial distribution.
has an approximately normal
distribution.
has a geometric distribution.
has a normal distribution.
has a Poisson distribution.
has an unknown 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 = 47. (Enter an exact number.)
z =
(c)
Find P( < 47). (Enter a
number. Round your answer to four decimal places.)
P( < 47)
= P(x bar < 47)
(d)
Would it be unusual for a random sample of
size 36 from the x distribution to
have a sample mean less than 47? Explain.
Yes, it would be unusual because more than 5% of all such
samples have means less than 47.
Yes, it would be unusual because less than 5% of all such
samples have means less than 47.
No, it would not be unusual because more than 5% of all such
samples have means less than 47.
No, it would not be unusual because less than 5% of all such
samples have means less than 47.