A distribution of grades in an introductory statistics class

A distribution of grades in an introductory statistics class (where A = 4, B = 3, etc) is:

X

0

1

2

3

4

P(X)

0.11

0.17

0.24

0.32

___

Part a: Find P(X = 4).
Part b: Find P(1 X < 3) .
Part c: Find the mean grade in this class.
Part d: Find the variance and standard deviation for the class grades.
Part e: Define a new variable Y = 4X + 1. Find the mean and variance of Y.

Question 9

Suppose that in a large metropolitan area, 90% of all households have a flat screen television. Suppose you are interested in selecting a group of six households from this area. Let X be the number of households in a group of six households from this area that have a flat screen television.

Part a: Show that this problem satisfies the requirements to be a binomial distribution.
Part b: For what proportion of groups will exactly four of the six households have a flat screen television?
Part c: For what proportion of groups will at most two of the households have a flat screen television?
Part d: What is the expected number of households that have a flat screen television?

Question 10

P(E) = 0.35, P(F) = 0.54, and P(E F) = 0.62

Part a: Find P(E F).
Part b: Find P(E | F).
Part c: Find P(F | E).
Part d: Are the events E and F independent?

Solution