The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution:

x	0	1	2	3	4	5
P(X = x)	0.20	0.30	0.20	0.15	0.10	0.05

On average, how many accidents are there in the intersection in a week?

1. 5.3
2. 2.5
3. 1.8
4. 0.30
5. 0.1667

Question 2Select one answer.10 points

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

X	3	6	9	12	15
P(X=x)	4/9	2/9	1/9	1/9	1/9

1. Yes, the values of X are all positive.
2. No, the values of X do not start at 1 and the probabilities do not add up to 1.
3. No, the probabilities do not add up to 1.
4. Yes, the probabilities associated with each X are all positive and they all add up to 1.

Question 3Select one answer.10 points

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

second questions \

question 1

For safety reasons, 3 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 3 systems detects theft with a probability of 0.84 independently of the others.

The bank, obviously, is interested in the probability that when a theft occurs,at least one of the 3 systems will detect it. What is the probability that when a theft occurs, at least oneof the 3 systems will detect it?

Your answer should be rounded to 5 decimal places.

Question 2

Type numbers in the boxes.

10 points

In a certain liberal arts college with about 10,000 students, 40% are males. If two students from this college are selected at random, what is the probability that they are of the same gender?

Your answer should be rounded to 4 decimal places.

Question 3

Type numbers in the boxes.

10 points

According to the information that comes with a certain prescription drug, when taking this drug, there is a 18% chance of experiencing nausea (N) and a 44% chance of experiencing decreased sexual drive (D). The information also states that there is a 11% chance of experiencing both side effects.

What is the probability of experiencing only nausea?

Your answer should be rounded to two decimal places. If you have trouble doing this problem, watch the video below: https://youtu.be/aN0eulm19MM

Question 4

Type numbers in the boxes.

10 points

According to the information that comes with a certain prescription drug, when taking this drug, there is a 25% chance of experiencing nausea (N) and a 40% chance of experiencing decreased sexual drive (D). The information also states that there is a 12% chance of experiencing both side effects.

What is the probability of experiencing neither of the side effects?

Your answer should be to two decimal places.

Question 5

Type numbers in the boxes.

10 points

According to the information that comes with a certain prescription drug, when taking this drug, there is a 18% chance of experiencing nausea (N) and a 49% chance of experiencing decreased sexual drive (D). The information also states that there is a 10% chance of experiencing both side effects.

What is the probability of experiencing nausea or a decrease in sexual drive?

Your answer should be rounded to 2 decimal places.

Question 6

Type numbers in the boxes.

10 points

An engineering school reports that 54% of its students are male (M), 33% of its students are between the ages of 18 and 20 (A), and that 28% are both male and between the ages of 18 and 20.

What is the probability of a random student being chosen who is a female and is not between the ages of 18 and 20?

Your answer should be to two decimal places.

Question 7

Type numbers in the boxes.

10 points

An engineering school reports that 50% of its students were male (M), 36% of its students were between the ages of 18 and 20 (A), and that 30% were both male and between the ages of 18 and 20.

What is the probability of choosing a random student who is a female or between the ages of 18 and 20? Assume P(F) = P(not M).

Your answer should be given to two decimal places.

Question 8

Type numbers in the boxes.

10 points

An engineering school reports that 59% of its students were male (M), 31% of its students were between the ages of 18 and 20 (A), and that 25% were both male and between the ages of 18 and 20.

What is the probability of a random student being male or between the ages of 18 and 20?

Your answer should be rounded to two decimal places.