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# Normal Distribution

ATMs must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend. But if too much cash is unnecessarily kept in the ATMs, the bank is foregoing the opportunity of investing the money and earning interest. Suppose that at a particular branch the population mean amount of money withdrawn from A

### Probability and normal distribution..

In planning for hot water requirements, the manager of the Luxurion Hotel finds that guests spend a mean of 11.4 minutes each day in the shower. Assume that the shower times are normally distributed with a standard deviation of 2.6 min. a. Find the percentage of guests who shower more than 12 minutes b. The hotel has instal

### Normal Probability Distributions Values

Applying Continuity Correction - The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. Probability of at least 12 adult males on an elevator in the Empire State Building Probability that the number of working vending

### Probability Based on Normal Distribution of Flu Symptoms

Cholesterol Reducing Drug - The probability of flu symptoms for a person not receiving any treatment is 0.019. In a clinical trial of lipitor, a common drug used to lower cholesterol, 863 patients were given a treatment of 10-mg atorvastatin tablets, and 19 of those patients experienced flu symptoms (based on data from Pfizer, i

### Standard normal distribution

Standard normal distribution - Assume the readings on the thermometers are normally distributed with a mean of 0° and a standard deviation of 1.00°c. A thermometer is randomly selected and tested. In each case draw a sketch, and find the probability of each reading. Greater than 1.96 Between 0.50 and 1.50 Between -3.

### 95th Percentiles of Normal Distribution

Suppose X ~ N(10,100) find the 10th and the 95th percentiles of X.

### Statistics - Multiple choice- Sampling, central limit theorem, normal distribution

Question 1 All of the following are reasons to sample except for: a) Reduce sampling error b) The research process is sometimes destructive. c) Save time d) For given resources, broaden the scope of the study. Question 2 Sampling in which every unit of the population has the same probability of being sel

### Statistics - Normal Distribution, Statistical test

1. The net profit of an investment is normally distributed with a mean of \$10,000 and a standard deviation of \$5,000. The probability that the investor's net gain will be at least \$5,000 is _____________. a) 0.4967 b) 0.8413 c) 0.1859 d) 0.3413 2. A company believes that it controls more

1 Research the typical categories of retirement annuity plans? 2. what is a 401 (k) plan? What is a Roth IRA ? How are they different ?Why were they developed? 3. How do they work? 4. Compare and contrast the features of the two types of retirement plans? 5. What are the advantages of pa

### Statistics - Geometric Distribution and Poisson Distribution

Question 1 The probability that you will make a sale on any given telephone call is 0.23. What is the probability that you do not make any sale on the first three calls? [Hint: geometric distribution] a. 0.105 b. 0.543 c. 0.457 d. 0.186 Question 2 The mean number of typographical error per page of a newspaper is 3. What

### Probability: Normal and Binomial Distributions

1. A component in a subsystem has a reliability factor of .9999 during a Shuttle mission. There is redundancy so as long as fewer than 2 of the components fail, the subsystem will operate. What is the probability that there will be 2 or more failures? 2. A video tube has a mean life of 2000 hours with a standard deviation of

### Coastal National Bank and Trust Online Mortgage Applications

In recent times, with mortgage rates at low levels, financial institutions have had to provide more customer convenience. One of the innovations offered by Coastal National Bank and Trust is the on-line entry of mortgage applications. Listed below is the time, in minutes, to complete the application process for customers applyin

### Continuous Probability Distribution Percentile Ranks

Jon Molnar will graduate form Caroling Forest High School this year. He took the American College Test (ACT) for college admission and received a score of 30. The high school principal informed him that only 2 percent of the students taking the exam receive a higher score. The mean score for all students taking the exam is

### Questions About Probabilities and Normal Distributions

A famous restaurant owner noticed that in the past 20 years his hamburger supply shows a normal distribution in weight. Average weight was 10.0 ounces with a standard deviation of 0.3 ounces after they were cooked. (Consider normal distribution) * What is a probability that a customer gets a hamburger that weighs at least 10.

### Multiple Choice

Question 1. If you have a normal distribution of a random variable x, with a mean of 56 and standard deviation of 8: What is the probability that the random variable x will be within plus or minus 1 standard deviation of the mean? a. 0.682 b. 0.75 c. 0.00 Question 2 What is the probability that x is greater than 64?

### Normal Distribution and Proportion of Scores. The solutions are given with each minute detail of their solution steps. These step by step solutions will help students to work out other similar problems on their own efforts.

Question (1) Scores on WAIS approximate a normal curve with a mean of 100 and standard deviation of 15. What proportion of scores are (i) Above 125 ? (ii) Below 82 ? (iii) Within 9 points of the mean ? (iv) More than 4o points from the mean ? Question (2) Scores on WAIS test approximately normal with a mean of 100 and

### Business Statistics -problems on two-sigma control limits, p charts, c charts

10. A travel agency is concerned with the accuracy and appearance of itineraries prepared for its clients. Defects can include errors in times, airlines, flight numbers, prices, car rental information, lodging, charge card numbers and reservation numbers, as well as typographical errors. As the possible number of errors is nearl

### Statistics: The Accounting Department at Weston Materials, Inc.

The accounting department at Weston Materials, Inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution. a. Determine the z values for 29 and

### Probability questions on Binomial and normal distribution

1. Assume a restaurant business succeeds 60% of the time. Suppose that there are three such restaurants open in your city. When they don?t compete with one another, it is reasonable to believe that their relative success would be independent. [Hint: use binomial probability distribution function in Megastat or Phstat] A) Wha

### Standard error and average catch of lobster fisherman

1. A survey of 250 lobster fisherman found that they catch an average of 32 pounds of lobster per day with a standard dev of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds? 2. The standard deviation of a distribution is 20. If a sa

### Standard Normal Distribution

The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. a. What is the area between 415 pounds and the mean of 400 pounds? b. What is the area between the mean and 395 pounds? c. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?

### Normal distribution

A recent study by the Greater Los Angeles Taxi Drivers Association showed that the mean fare charged for service from Hermosa Beach to the Los Angeles International Airport is \$18.00 and the standard deviation is \$3.50. We select a sample of 15 fares. 1. What is the likelihood that the sample mean is between \$17.00 and \$20.00?

### Inventory Models

Managers at Wager Fabricating Company are reviewing the economic feasibility of manufacturing a part that it currently purchases for a supplier. Forecasted annual demand for the part is 3200 units. Wagner operates 250 days per year. Wagner's financial analysts have established a cost of capital of 14% for the use of funds f

### Probability

1. MCQ: The first test in Introductory Algebra had a mean of 82 with a standard deviation of 15. If a student made a 94 on the test, what is the corresponding z-score? a) -0.58 b) -0.47 c) 0.47 d) 0.80 e) NOT 2. Students are sorted according to sex (male, female), grade level (lower division, up

### Two Normal Distribution Papers

(See attached files for full problem description).

### Standard deviation of the winning percentages in a league: Compare the 5 values of standard deviation that you determined for each league. What does this suggest about competitive balance in the two leagues? Explain.

A) For the two hypothetical leagues represented below calculate the league standard deviation (s t) of the winning percentage (wti) for each year. {Where wti is the winning percentage of team i in year t; st is the standard deviation of the winning percentages in one of the leagues in year t; and w is calculated as the number of

### % of cruises for normal distribution and standard deviation

The number of passengers on the Carnival Sensation during one-week cruises in the Caribbean follows the normal distribution. The mean number of passengers per cruise is 1,820 and the standard deviation is 120. a. What percent of the cruises will have between 1,820 and 1,970 passengers? b. What percent of the cruises will h

### Long distance calling and food expenditures based on a normal distribution

Problem 1 A recent report in USA Today indicated a typical family of four spends \$490 per month on food. Assume the distribution of food expenditures for a family of four follows the normal distribution, with a mean of \$490 and a standard deviation of \$90. a. What percent of the families spend more than \$30 but less than \$490

### expected value and variance of random variable

Please see the attached file "Q11.5.doc" for the problem statement. suppose that w is normal and has expected value a and variance sigma^2. so the expected value of u = exp(w) is exp(a + 0.5sigma^2). What is the variance of u: var(u)?

### Important information about Normal distribution probability

The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, with a mean of \$70,000 and a standard deviation of \$20,000. A loan application is received this morning. What is the probability? a. The amount requested is \$80,000 or more? b. The amount requested is between