Determine if the following could be a probability distribution for a discrete random variable, X. If no, state why.

X	20	30	40	50
P(X=x)	1.1	0.6	.2	.1

1. No, while the probabilities are all positive, the P(X=20)=1.1. Probabilities cannot exceed 1.
2. Yes, the probabilities are all positive.
3. No, the values of X are too far apart and the probabilities add up to a value greater than 1.
4. Yes, the probabilities add to 1 and they are all positive.

Question 4Type numbers in the boxes.Part 1:2 pointsPart 2:2 pointsPart 3:2 pointsPart 4:2 pointsPart 5:2 points10 points

Below is a distribution for number of visits to dentists in one year.

X	1	2	3	4	5
P(X=x)	0.29	0.42	0.19	0.06	0.04

Calculate the following probabilities:

a. P(X < 2) =

b. P(X3) =

c. P(1< X3) =

d. P(3X < 5) =

e. P(3 < X < 5) =

Question 5Type numbers in the boxes.Part 1:2 pointsPart 2:2 pointsPart 3:2 pointsPart 4:2 pointsPart 5:2 pointsPart 6:2 points12 points

Below is a probability distribution for the number of failures in an elementary statistics course.

X	0	1	2	3	4
P(X=x)	0.41	0.18	?	0.05	0.13

Determine the following probabilities:

a. P(X = 2) =

b. P(X < 2) =

c. P(X2) =

d. P(X > 2) =

e. P(X = 1 or X = 4) =

f. P(1X4) =

Question 6Type numbers in the boxes.Part 1:5 pointsPart 2:5 points10 points

From past experience, a company has found that in carton of transistors:

92% contain no defective transistors

3% contain one defective transistor,

3% contain two defective transistors, and

2% contain three defective transistors.

Calculate the mean and variance for the defective transistors.

Mean =

Variance =

(Please round answers to 4 decimal places.)

Question 7Select one answer.10 points

First, find the value of the constant,kso that the following table represents a probability distribution for the random variable,xand then findP(x<2).

x	0	1	2	3
P(x)	2k	3k	13k	2k

The probability that P(X < 2) is equal to

1. 0.90
2. 0.15
3. 0.25
4. 1.00
5. 0.65

Question 8Type numbers in the boxes.Part 1:4 pointsPart 2:4 pointsPart 3:2 pointsPart 4:2 points12 points

A florist determines the probabilities for the number of flower arrangements they deliver each day.

x	19	20	21	22	23
P(x)	0.23	0.21	0.30	0.15	0.11

Find the mean, variance, and standard deviation of the distribution rounded to 4 decimal places.

Mean =

Variance =

Standard Deviation =

Approximately how many arrangements should the florist expect to deliver each week, rounded to the nearest whole number?