Suppose x has a distribution with a mean of 70 and a standard deviation of 45. Random samples of size n = 36 are drawn. (a)

Describe the distribution.

has a binomial distribution. has a Poisson distribution. has an unknown distribution. has a geometric distribution. has a normal distribution. has an approximately normal 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 = 55. (Enter an exact number.)

z =

(c)

Find P( < 55). (Enter a number. Round your answer to four decimal places.)

P( < 55) = P(x bar < 55)

(d)

Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 55? Explain.

Yes, it would be unusual because more than 5% of all such samples have means less than 55. No, it would not be unusual because less than 5% of all such samples have means less than 55. Yes, it would be unusual because less than 5% of all such samples have means less than 55. No, it would not be unusual because more than 5% of all such samples have means less than 55