Which of the following is NOT a property of the Student t distribution?

Choose the correct answer below.

O A. The Student t distribution has a mean of t= 0.

O B. The Student t distribution has the same general symmetric bell shape as the standard normal distribution, but it reflects the greater variability that is expected with

small samples.

• C. The Student t distribution is different for different sample sizes.

O D. The standard deviation of the Student t distribution is s = 1

The graph below shows three different normal distributions. Which statement is true?

a.) Each distribution has a different mean and the same standard deviation.

b.) Each distribution has a different mean and a different standard deviation.

c.) Each distribution has the same mean and the same standard deviation.

d.) Each distribution has the same mean and a different standard deviation.

Which of the following is not a conclusion of the central limit​ theorem?

A) The distribution of the sample means ​will, as the sample size​ increases, approach a normal distribution.

B) The distribution of the sample data will approach a normal distribution as the sample size increases.

C) The standard deviation of all sample means is the population standard deviation divided by the square root of the sample size.

D) The mean of all sample means is the population mean μ.

The overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 8.3 cm.

a. Find the probability that an individual distance is greater than 214.80 cm.

b. Find the probability that the mean for 20 randomly selected distances is greater than 203.70 cm.

c. Why can the normal distribution be used in part b, even though the sample size does not exceed 30?

a. The probability is ____.

(Round to four decimal places s needed.)

b. The probability is ____.

(Round to four decimal places as needed.)

c. Choose the correct answer below.

◯ A. The normal distribution can be used because the original population has a normal distribution.

◯ B. The normal distribution can be used because the finite population correction factor is small.

◯ C. The normal distribution can be used because the mean is large

◯ D. The normal distribution can be used because the probability is less than 0.5