University of Massachusetts Dartmouth Normal Distribution Questions

•QUESTION 8 Multiple choice
•
Suppose x has a distribution with µ = 32 and σ = 16.
(a) If random samples of size n = 16 are selected, can we say anything about the x distribution of
sample means?
No, the sample size is too small.
•
Yes, the x distribution is normal with mean = 32
andx=distribution
16.
Yes, the
is normal with mean = 32
andx distribution
= 1.0
Yes, the
is normal with mean = 32
and = 4
3 points
QUESTION 9 Multiple choice
•
Suppose x has a distribution with µ = 32 and σ = 16.
(b) If the original x distribution is normal, can we say anything
about the x distribution of random samples of size 16?
Yes, the x distribution is normal with mean
and
= 16
Yes, the
x distribution
is normal with mean
and
= 1.0
Yes, the
x distribution
is normal with mean
and
= 4.size is too small.
No, the
sample
= 32
= 32
= 32
•
3 points
QUESTION 10
•
Suppose x has a distribution with µ = 32 and σ = 16. If the
original x distribution is a normal and random samples of size 16 are
drawn:
Find P(26 < x < 35). (Use the tables from the textbook and state your answer to four decimal places.) P(26 < x < 35) = P( ____< z < ____) = _______ 9 points QUESTION 11 • • • • • Consider an x distribution with standard deviation σ = 44. (a) If specifications for a research project require the standard error of the corresponding distribution to be 4, how large does the sample size need to be? n= (b) If specifications for a research project require the standard error of the corresponding distribution to be 1, how large does the sample size need to be? n= 6 points QUESTION 12 • Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard deviation 4 inches. (Use the textbook tables and state probability to four decimal places.) (a) What is the probability that an 18-year-old man selected at random is between 65 and 67 inches tall? • P(65 < < 67) = P( ____< z < ____) = _______ (b) If a random sample of nine 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches? P(65 < < 67) = P( ____< z < ____) = _______ 12 points QUESTION 13 Multiple choice • Compare your answers to parts (a) and (b) in the previous problem. Is the probability in part (b) much higher? Why would you expect this? The probability in part (b) is much lower because the standard deviation for thebecause distribution. The probability in part (b)isissmaller much higher the standard deviation for thebecause distribution. The probability in part (b)isissmaller much higher the mean is larger for(b) the distribution. The probability in part is much higher because the standard deviation is larger for the distribution. • •