Chapter 4 – Probability

A bag contains 6 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag:

1. What is the probability that it is blue?
2. What is the probability that it is green?
3. What is the probability that it is red?
4. What is the probability that it is yellow?
5. What is the probability that is blue or green?
6. What is the probability that is red or green?
   A bag contains 4 purple marbles, 10 yellow marbles, and 8 orange marbles. If two marbles are selected from the bag:
7. What is the probability that an orange then a yellow are chosen with replacement?
8. What is the probability that a purple then an orange are chosen without replacement?
9. What is the probability that two yellows are chosen with replacement?
10. What is the probability that two yellows are chosen without replacement?
    Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05.
11. Assume that one student in your class of 27 students is randomly selected to win a prize. Would it be "unusual" for you to win?

Chapter 5 – Discrete Probability Distributions

1. What is a probability distribution? What are the two requirements of it?
2. Is the following a probability distribution? If yes, find the mean and standard deviation using the table.

   x	P(x)	\[x\cdot P(x)\]	\[{{x}^{2}}\]	\[{{x}^{2}}\cdot P(x)\]
   0	0.23
   1	0.43
   2	0.34
   Total		Total=		Total=
   		\[{{\mu }^{2}}=\]		\[{{\sigma }^{2}}=\]

   
   \[\mu =\] ______ \[\sigma =\] ______
3. Is the following a probability distribution? If yes, find the mean and standard deviation using the table.

   x	P(x)	\[x\cdot P(x)\]	\[{{x}^{2}}\]	\[{{x}^{2}}\cdot P(x)\]
   0	0.15
   1	0.52
   2	0.32
   Total		Total=		Total=
   		\[{{\mu }^{2}}=\]		\[{{\sigma }^{2}}=\]

   
   \[\mu =\] ______ \[\sigma =\] ______
4. Is the following a probability distribution? If yes, find the mean and standard deviation using the table.

   x	P(x)	\[x\cdot P(x)\]	\[{{x}^{2}}\]	\[{{x}^{2}}\cdot P(x)\]
   0	0.18
   1	0.32
   2	0.27
   3	0.23
   Total		Total=		Total=
   		\[{{\mu }^{2}}=\]		\[{{\sigma }^{2}}=\]

   
   \[\mu =\] ______ \[\sigma =\] ______
5. Calculate the probability of the following binomial distribution using the formula.
   n = 5, x = 4, p = 0.2, q = 0.8 \[P(x)=\frac{n!}{(n-x)!x!}\cdot {{p}^{x}}\cdot {{q}^{n-x}}\]
6. A procedure is repeated n = 6 times, use table A – 1 to find the probability of x = 5 successes given the probability p = 0.99 of success on a given trial.
7. Calculate the probability of the following binomial distribution using the formula.
   n = 6, x = 2, p = 0.45
8. A procedure is repeated n = 11 times, use table A – 1 to find the probability of x = 7 successes given the probability p = 0.50 of success on a given trial.
9. Use the values of n = 186 and p = 0.13 to find the minimum and maximum usual values for this binomial distribution.

Chapter 6 – Normal Probability Distributions

Use the following uniform density curve to answer the problems 1 to 4. Start by calculating the appropriate "width".

P(x)

?

0 2.5 5 x

1. What is the probability that the random variable has a value greater than 0.4?
2. What is the probability that the random variable has a value less than 2.0?
3. What is the probability that the random variable has a value between 1.5 and 3.5?
4. What is the probability that the random variable has a value between 1.0 and 4.5?
5. Find the probability of a randomly selected value is less than 1.67?
6. Find the probability of a randomly selected value is less than –2.12?
7. Find the probability of a randomly selected value is greater than 0.6?
8. Find the probability of a randomly selected value is greater than 2.45?
9. Find the probability of a randomly selected value is greater than –1.61 but less than 1.61?
10. Find the z score that corresponds to the 86 ^th percentile.
11. Find the z score that corresponds to the area of 0.3461.
12. Find the values separating the top 5% and the bottom 5%. What percentage of values will fall between these scores?
13. Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a standard deviation of 1.1 years. Find the probability that a randomly selected washing machine will have a replacement time less than 9.1 years.
14. A final exam in Math 260 is normally distributed and has a mean of 73 with a standard deviation of 7.8. If a student is randomly selected, find the probability that their test score is less than 75.
15. Using the mean and standard deviation from the previous problem, find the test score that will separate the bottom 90% from the top 10%.

Price: $26.42

Solution: The downloadable solution consists of 14 pages, 1242 words and 18 charts.
Deliverable: Word Document