Author Question: Think of the situation of rolling two dice and let M denote the sum of the number of dots on the two ... (Read 144 times)

KWilfred · **on:** Jun 29, 2018

Think of the situation of rolling two dice and let M denote the sum of the number of dots on the two dice. (So M is a number between 1 and 12.)

(a) In a table, list all of the possible outcomes for the random variable M together with its probability distribution and cumulative probability distribution. Sketch both distributions.
(b) Calculate the expected value and the standard deviation for M.
(c) Looking at the sketch of the probability distribution, you notice that it resembles a normal distribution. Should you be able to use the standard normal distribution to calculate probabilities of events? Why or why not?
What will be an ideal response?

Question 2

You are at a college of roughly 1,000 students and obtain data from the entire freshman class (250 students) on height and weight during orientation.

You consider this to be a population that you want to describe, rather than a sample from which you want to infer general relationships in a larger population. Weight (Y) is measured in pounds and height (X) is measured in inches. You calculate the following sums:

= 94,228.8, = 1,248.9, = 7,625.9

(small letters refer to deviations from means as in = ).

(a) Given your general knowledge about human height and weight of a given age, what can you say about the shape of the two distributions?
(b) What is the correlation coefficient between height and weight here?
What will be an ideal response?

lkoler · **Reply #1 on:** Jun 29, 2018

Answer to Question 1

Answer:
(a)

(b) 7.0; 2.42.
(c) You cannot use the normal distribution (without continuity correction) to calculate probabilities of events, since the probability of any event equals zero.

Answer to Question 2

Answer:
(a) Both distributions are bound to be normal.
(b) 0.703.