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# Normal Distribution

### Mensa - Normal Distribution

To become a member of Mensa, one has to pass the qualifying exam. If the scores on the exam are normally distributed with a mean of 80 and a standard deviation of 25, and if only the top 20% of the people taking the exam are admitted, what is the passing score?

1. R.C. Geary wrote some 70 years ago that "Normality is a myth. There never was, is, nor will there ever be a Normal distribution". What do you think he meant and what relevance does it have to your work?(Read the Week 2 Lecture 1 before answering) 2.How do you feel that the inferential statistical technique of Hypothesis Te

### Normal approximation to the bionomial distribution

11% of all books sold are romance genre. If the bookstore sells 316 books on a given day, what is the probability that fewer than 40 are romances, at least 25 are romances, between 25 and 40 are romances? What is n?p?q? Are both np and nq larger than 5? Why is this important to consider?

### Statistics - Normal Distribution for Z Scores

Assuming that x has a normal distribution, find the indicated probability a) p(40<_x<_47) mean=50, stand.dev.=15 and p(x_>2)mean=3stand.dev.=0.25 b) Find z value and sketch the are described 1) 97.5%of normal curve lies to the left of z 2) Find z such that 95% of standard normal curve lies to the right of z

### How much should a healthy kitten weigh?

How much should a healthy kitten weigh? A healthy 10-week-old (domestic) kitten should weigh an average of mu = 23.5 oz with 95% of data ranging from 13 to 34 oz. Let x be a random variable that represents the weight (in ounces) of a healthy 10-week-old kitten. Assume that x has a distribution that is approximately normal. m

### Normal Distribution and Z-Scores

1. For each of the following z-scores, sketch a normal distribution and draw a vertical line at the location of the z-score. Then, determine whether the tail is to the right or the left of the line and find the proportion in the tail. a. z = 2.00 b. z = 0.50 c. z = -1.00 d. z = -0.75. 2. The distribution of score

### Grading Egg Sizes - Normal Distribution

In grading eggs into small, medium and large, Margi farms packs the eggs that weigh more than 4.25 ounces in packages marked " large" and the eggs that weigh less than 2.45 ounces in packages marked " small" the remainder are packed in packages marked " medium". If a day's packaging contained 10.56% large and 4.01% small eggs, c

### The Wall Street Journal reported some interesting statistics on the job market. ...

The Wall Street Journal reported some interesting statistics on the job market. One statistic is that 40% of all workers say they would change jobs for "slightly higher pay." In addition, 88% of companies say that there is a shortage of qualified job candidates. Suppose 16 workers are randomly selected and asked if they would ch

### Tompkins Associates reports that the mean clear height for a Class A warehouse in the Unites States is 22 feet. ...

Tompkins Associates reports that the mean clear height for a Class A warehouse in the Unites States is 22 feet. Suppose clear heights are normally distributed and that the standard deviation is 4 feet. A Class A warehouse in the Unites States is randomly selected. a. what is the probability that the clear height is greater t

### Cable Companies - Normal Distribution

According to the Yankee group, 53% of all cable households rate cable companies as good or excellent in quality transmission. Sixty percent of all cable households rate cable companies as good or excellent in having professional personnel. Suppose 300 cable households are randomly contacted? a. What is the probability that m

### Fresh Fruit Consumption - Normal Distribution

The Statistical Abstract of the United States published by the US Census Bureau reports that the average annual consumption of fresh fruit per person is 99.9 pounds. The standard deviate of fresh fruit consumption is about 30 pounds. Suppose a researcher took a random sample of 38 people and had them keep a record of the fresh f

The Travel Weekly International Air Transport Association survey asked business travelers about the purpose for their most recent business trip. 19% responded that it was for an internal company visit. Suppose 950 business travelers are randomly selected. a. What is the probability that more than 25% of the business traveler

### A criminologist has developed a test to measure self-control. The test is normed so that it has a mean of 70 and a standard deviation of 20. The scores are normally distributed ...

A criminologist has developed a test to measure self-control. The test is normed so that it has a mean of 70 and a standard deviation of 20. The scores are normally distributed in the population of college students used to develop the test. a. What is the percentile rank of a score of 40? b What percentage of scores falls be

### Area under standard normal curve - Part 1) Sketch area under standard normal curve over the indicated intervals, and find the specified area. ...

Part 1) Sketch area under standard normal curve over the indicated intervals, and find the specified area. a) to the left of z=0.15 b) to the right of z=-2.17 c) between z=-1.40 and z=2.03 Part 2) Let z be a random variable with standard normal distribution. Find indicated probability and shade corresponding area under the

### A union of restaurant and foodservice workers would like to estimate the mean hourly wage,(m), of foodservice workers in the U.S. The union will choose a random sample of wages and then estimate (m) using the mean of the sample. What is the minimum sample size needed in order for the union to be 99% confident that its estimate is within \$0.45 ...

A union of restaurant and foodservice workers would like to estimate the mean hourly wage,(m), of foodservice workers in the U.S. The union will choose a random sample of wages and then estimate (m) using the mean of the sample. What is the minimum sample size needed in order for the union to be 99% confident that its estimate i

### Combinations and Percentage Probabilities

5.50 A tax account has three choices for the method of treating one of a client's deductions. After this choice has been made, there are only two choices for how a second deduction can be treated. What is the total number of possibilities for the treatment of the two deductions? 5.51 A committed consists of eight members

### Statistics - Suppose that x has adistribution ... [See the attached Question Fiel.]

Suppose that x has adistribution ... [See the attached Question Fiel.]

### Normal Distribution and Probability..

The expected return and standard deviation of returns of General Mills common stock over the next year are estimated to be 20 percent and 12 percent, respectively. Assume that the returns are approximately normally distributed. a. Determine the probability of incurring a loss (negative rate of return) from investing in this st

### Inverse Normal Distribution SAT and ACT Scores - For a given population of high school seniors, the schoolastic aptitude test (SAT) in mathemathics has a mean score of 500 with the standard deviation of 100. Another widely used test is the American college testing (ACT)exam. The mathemathics portion of the ACT mean of 18 and a standard deviation of 6 ...

For a given population of high school seniors, the schoolastic aptitude test (SAT) in mathemathics has a mean score of 500 with the standard deviation of 100. Another widely used test is the American college testing (ACT)exam. The mathemathics portion of the ACT mean of 18 and a standard deviation of 6. (a) Suppose that an en

### Medical: Blood Protoplasm - Porphyrin is a pigment in blood

Medical: Blood Protoplasm - Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy adults x is approximately normally distributed with the mean &#956;= 38

### Probability calculations using Normal Distribution

Assume X has a normal distribution, with the specified mean and standard deviation. Find the indicated probabilities. 6. P(40 <= x <= 47) M = 50; s = 15 10. P(x >= 2); M = 3; s = 0.25 14. Find z such that 97.5% of the standard normal curve lies to the left of z. 18. Find z such that 95% of the standard normal curv

### Sensitivity, Specificity and Predictive Value

Please see the attached file. 1. Directions: A screening test for breast cancer was administered to 400 women with biopsy-proven breast cancer and to 400 normal women without breast cancer. The screening test results were positive for 100 of the biopsy-proven cases and 50 of the normal women. Question 1: The sensit

### Trading strategies involving options: Provide a table showing the relationship between the profit and final stock price for the following: bull spread using European call options, bear spread using European put options, butterfly spread using European call options, butterfly spread using european put options, straddle using options, strangle using options

Suppose that the price of a non-dividend paying stock is \$32, its volatility is 30%, and the risk-free rate for all maturities is 5% per annum. Use derivagem to calculate the costs of setting up the following positions. In each case provide a table showing the relationship between the profit and final stock price. Ignore the imp

### The score on the entrance test for a well known law school has a mean score of 200 points

The score on the entrance test for a well known law school has a mean score of 200 points and a standard deviation of 50 points. At value should the lowest passing score be set if the school wishes only 2.5% of those taking the entrance test to pass?

### Statistics - Normal Distribution: Four Questions

1. If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the point in the distribution in which 75.8% of the college students exceed when trying to find a parking spot in

### Normal Distribution and Probability

1. Suppose a sample of n = 50 items is drawn from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a probability distribution with mean = 6 ounces and standard deviation= 2.5 ounces. Which of the following is true about the sampling distribution

### Normal distribution, mean, standard deviation, sampling distribution

The World Health Organization has reported that systolic blood pressures of Canadians are normally distributed with a mean of 121 and a standard deviation of 16. What symmetric interval about the mean will contain approximately 95% of the systolic blood pressure readings for Canadians? A. 105

### Quantitative Methods Homework

Hello, Here are three quantitative methods problems. Thanks! -------------------------------- Prob 1 Bill and Joe are playing a match in which the first player to win 2 games wins the match. For any given game, the probability that Bill wins is 1/3. (a) Find the probability that Bill wins the match. (

### Find the indicated probability.

Find the indicated probability. 4) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275. 5) In one region, the September energy consumption l

### If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes

1. If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in les