Question

1. Suppose x has a distribution with a mean of 20 and a standard deviation of 3. Random samples of size n = 36 are drawn.
   1. Is the sampling distribution of x normal? How do you know?

2. What is the mean and the standard deviation of the sampling distribution of x?

3. Find the z score corresponding to x = 19.

4. Find P (x < 19).

5. Would if be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 19? Why?

Answer 1

Solution :

(a)

sampling distribution of x normal because n > 30 .

(b)

The sampling distribution of mean is ,

= 20

The sampling distribution of standard deviation is ,  

= / n = 3 / 36 = 0.5

(c)

z = (19 - 20) / 0.5 = -2

(d)

P(z < -2) = 0.0228

(e)

It can be unusual because the probability is less than 0.05