Suppose x has a distribution with a mean of 40 and a standard deviation of 21. Random samples of size n = 36 are drawn.
a) Describe the
x̅ distribution.
x̅ has a geometric distribution
x̅ has a Poisson distribution.
x̅ has an unknown distribution
x̅ has a normal distribution
x̅ has an approximately normal distribution
x̅ has a binominal distribution
Compute the mean and standard deviation of the distribution. (For each answer, enter a number)
ux̅ =
ox̅ =
b) Find the z value corresponding to x̅ = 47 (Enter an exact number)
z =
c) Find P(x̅
< 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?
Yes, it would be unusual because less than 5% of all such samples have means less than 47
Yes, it would be unusual because more 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