Question

Page 1 Question 1 Suppose we take repeated random samples of size 20 from a population with a Select all that apply. mean of 60 and a standard deviation of 8. Which of the following statements is 10 points true about the sampling distribution of the sample mean (x)? Check all that apply. A. The distribution is normal regardless of the shape of the population distribution, because the sample size is large enough. B. The distribution will be normal as long as the population distribution is normal. C. The distribution's mean is the same as the population mean 60. D. The sampling distribution's standard deviation is larger than the population standard deviation of 8.

Answer 1

Solution:-

1. option A. The distribution will be normal as long as the population distribution is normal.
option C. The distribution's mean is the same as the population mean 60.

3. option D.it is extreamly unlike for this to occur;the probability is very close to 0.
Explanation : P(diff > 4) = P(Z > 4) = P(Z>4) =0.0000

4.option B. We take repeated random samples of size 15 from a population that is normally distributed.
option C. We take repeated random samples of size 50 from a population of unknown shape.

5. P(X < 4.2) = P(Z < (4.2-4)/(1.1/sqrt(100)) = 0.9656