Question

8.1.15-T Ra A simple random sample of size n 64 is obtained (a) Describe the sampling distribution of x. (b) What is P (x>90.8)? (c) What is P (xs 73.2)? (d) What is P (78.6 <x<90.2)? from a population with #8 3 and 32. (a) Choose the correct description of the shape of the sampling distribution of x. O A. The distribution is uniformm. O B. The distribution is skewed left O C. The distribution is approximately normal. O D. The distribution is skewed right O E. The shape of the distribution is unknown.

Answer 1

a) Since the sample size is large (>30), the distribution of sample mean will be approximately normal.

Option C is correct.

b) P(Mean > 90.8)

= P(z > 1.95)

= 0.0256

c) P(Mean < 73.2)

$= P(z < \frac{73.2-83}{32/\sqrt{64}})$

= P(z < -2.45)

= 0.0071

d) P(78.6 < Mean < 90.2)

$= P(\frac{78.6 - 83}{32/\sqrt{64}} < z < \frac{90.2-83}{32/\sqrt{64}})$

= P(-1.1 < z < 1.8)

= 0.8284