Supposexhas a distribution with a mean of30and a standard deviation of12. Random samples of sizen=64are drawn.(a) Describe thedistribution. 1. has a Poisson distribution. has a normal distribution.

2. has an unknown distribution. has a geometric distribution.

3. has a binomial distribution.

4. 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 thezvalue corresponding to=27. (Enter an exact number.) z= (c) FindP(<27). (Enter a number. Round your answer to four decimal places.) P(<27) =P(x bar < 27) (d) Would it be unusual for a random sample of size64from thexdistribution to have a sample mean less than27? Explain. 1. Yes, it would be unusual because less than 5% of all such samples have means less than 27.

2. No, it would not be unusual because less than 5% of all such samples have means less than 27.

3. Yes, it would be unusual because more than 5% of all such samples have means less than 27.

4. No, it would not be unusual because more than 5% of all such samples have means less than 27