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# Probability

### Determining Probability: Hair Dryer Example

The life expectancy of a brand of hair dryer is normally distributed with a mean of 4 years and a standard deviation of 8 months. a. What is the probability that the hair dryer will be in working condition for more than 5 years? b. What is the minimum and maximum life expectancy of the middle 90% of hte hair dryers?

### Probability of diameter

Please show calculations on how it's done. Sun Love grapefruit growers have determined that the diameters of their grapefruits are normally distributed with a mean of 4.5 inches and a standard deviation of 0.3 inches. If a grapefruit is selected at random, what is the probability that its diameter: a. is at least 4.14 in

### Expected Return for Stocks

(Excel: Calculating means, standard deviations, covariance, and correlation) Given the probability distributions of returns for stock X and stock Y, compute: a. the expected return for each stock, and here RETURNS Probability Stock X Stock Y 0.2 5% 12% 0.2 10 10 0.4 12 8 0.15 14 0 0.05 18 2

### Project's Return for Procter & Gamble

(Expected return and risk) Procter & Gamble is considering three possible capital investment projects. The projected returns depend on the future state of the economy as given here. a. Calculate each project's expected return, variance, and standard deviation. b. Rank the projects on the basis of (1) expected return and (2)

### Probability

Of a group of patients 28% visit both a physical Therapist (A) and a chiropractor (B). 8% visit neither. The probability of visiting (A) exceeds the probability of visiting (B) by 16%. What is the probability of a randomly selected person from this group visiting (A)

### Statistics - Probability for Johnson Space Center

A Johnson Space Center analysis estimated a 1 in 71 chance of losing the International Space Station to space debris or a meteoroid hit. (a) What kind of probability is this? Explain. (b) What is the probability of losing the station in this way?

### Probability of Adults Owning Stocks

A study for McNeil Associates for the NYSE revealed that 43% of all US Adults are stockholders. In addition the study determined that 75% of all US adult stockholders have some college education. Suppose 37% of all US adults have some college education. A US adult is randomly selected. a. What is the probability that the

### Probability

According to the US Bureau of Labor Statistics, 75% of the women 25 through 49 years of age participate in the labor force. Suppose 78% of the women in that age group are married. Suppose also that 61% of all women 25 through 49 years of age are married and are participating in the labor force. a. What is the probability that

### Quantitative Methods Coin Toss Simulation

Activity 18.1 1. Toss a coin 10 times, and after each toss record in the following table the result of the toss and the proportion of heads so far. For example, consider the sequence of tosses: H T T T H. After the first toss, the proportion of heads was 1/1, after the second the proportion of heads was 1/2, then after th

### Application of Poisson distribution

During the period of time phone-in reservations are being taken at a local university, calls come in at a rate of one every ten minutes. a. What is the expected number of calls in one hour? b. What is the probability of 4 calls in 5 minutes? c. What is the probability of 5 calls in a ten minute period?

### Problems with the binomial distribution formula

A foreman at a large plant estimates that parts are defective about 1% of the time. Use a binomial distribution formula to determine the mean number of defective parts if the plant produces 25,000 parts in a week.

### Distribution Formula

A tire manufacturer knows that about 5% of its tires are defective. Use a binomial distribution formula to determine if 12 tires are selected at random, what is the probability that 3 of them are defective?

### Proper probability distribution.

Determine whether each of the following is a proper probability distribution. If it is not, why? a. X 0 5 10 15 20 P(X) 1/4 1/2 1/3 -1/4 1/4 b. X 0 2 4 6 P(X) 1 1.5 0.3 0.2 c. X 1 2 3 P(X) 1/4 1/2 1/4 d. X -2 3 7

### Probability: Independent/Exclusive Events

See the attached file. 1) Let A and B be two events. a) If the events A and B are mutually exclusive, are A and B always independent? If the answer is no, can they ever be independent? Explain b) If A is a subset of B, can A and B ever be independent events? Explain 2) Flip an unbiased coin five independent times. Compute

### Probability

Hospital records indicated that maternity patients stayed in the hospital for the number of days shown in the following table: # of days (X) P(X) 1 0.29 2 0.25 3 0.17 4 0.15 5 or more 0.14 Find the probability t

### Probability of receiving scholarship

John Wells has applied for scholarships to two universities. The probability that he will receive a scholarship from University A is 0.55; the probability that he will receive a scholarship from University B is 0.65. the probability that he will receive scholarships from both is 0.4. a. What is the probability that he will

A survey of 254 students showed that 155 of them received academic awards, 152 received athletic awards, and 110 received both. What is the probability that a student received at least one of the two awards? What is the probability that a student did not receive either of these awards? Suppose a salesperson makes a sale

### Experimental Outcomes

Please show me work on how it's done. Thank you. Suppose that we have a sample space with 5 equally likely experimental outcomes: E1, E2, E3, E4 and E5. Let A={E1, E2}, B={E3, E4},a dn C={E3, E4, E5} a. Find P(A), P(B), P(C) b. Find P(A***B). Are A and B mutually exclusive? c. Find P(C^C) and P(A U C) *** is the

### Fast Service Truck Lines: Travelled Miles

Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made a study of the maintenance costs and determined the number of miles traveled during the year followed the normal distribution. The mean of the distribution was 60,000 miles and the standard deviation 2,000 miles. a. What percent of the Ford S

### Probability An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of two emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution.

An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of two emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution. a. What is the probability Linda Lahey, company president, received exactly 1 email between 4 P.M.

### Various Online Math Applications

Using a favorite Internet search source, conduct a general online Internet search for "math applications" in a chosen field of interest (for example, "math applications sports" or "math applications computers"). Your search should initiate several websites related to this topic. Visit several of these websites and browse t

### Coin Toss Probability

In this activity, you will explore some ideas of probability by using Excel to simulate tossing a coin and throwing a free throw in basketball. Toss a coin 10 times and after each toss, record in the following table the result of the toss and the proportion of heads so far. For example, suppose you obtain the following sequence

### Data Set Probability for Satisfied Individuals

Using our data set from Unit 1, compose an email to the head of the American Intellectual Union which discusses the following: Begin your email to AIU by first providing an overview of the database, i.e. a story. Be sure to include information about how you would use the concept of probabilities to apply to profiles for

### Combination and Permutation

1.3-1 There are total 8 digits and we wants to choose 4 digit from 8 digits for locks. Since in the number lock, we may choose combinations of repeated numbers. Thus first digit can be chosen from 8 ways. Since other second, third and fourth digits can be chosen from 8 ways . 1.3-2 since there are 4 Orchids we choos

### Business Statistics-probability question

An MBA graduate is applying for nine jobs, and believes that she has in each of the nine cases a constant and independent 0.48 probability of getting an offer. a. What is the probability that she will have at least three offers? b. If she wants to be 95% confident of having at least three offers, how many more jobs should she

### Calculation of Binomial Probability

10. A professor is giving a T/F test in your history class. Statistics show students who do not study for the test but attend class have a 70% chance of getting the answers correct. The test is 20 questions and the student did not study. (Hint: Binomial Distribution) a. What are the odds a student gets more than 13 question

### Probability Manufacturer to Reduce Codes

8. You just bought a new safe: It has a key pad with 26 letters on it. The code is 4 random letters a. How many different codes are there for you to select from if no letter can be used more than once? b. If no letter can be used more than once. Does Order Matter? c. If the manufacturer decided to reduce the code from

### Probability Frequency Definition

2. The table below represents the results of a survey of 1000 workers in Q1 2009 as to which benefit they find is the most important. Retirement Benefits are most important Health Benefits are most important Single 280 200 Married 220 300 a. If a Worker is chosen at random, what is

### Determining the Probability of a Certain Weight

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. If we select one box of cereal at random from this population, what is the probability that it will weigh less than 900 grams? Show work.

### Expected profit for the ski resort

Ski resort profits \$1,500,000 during a good winter with lots of snow. The resort has a loss of \$500,000 otherwise. The resort's historical climate data suggests that the probability of a good winter with lots of snow during any given year is 40%. What is the expected profit for the ski resort?