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Normal Distribution

Independent Random Samples

Let X and Y be the respective means of two independent random samples, each of size 4, from the two respective normal distributions N( 10, 9) and N(3, 4). Compute Pr (X > 2 Y).

Sample Mean

The mean annual salary for employees at Company X is $78,000. If we assume a standard deviation of $12,000, what is the sampling distribution of the sample mean for samples of size 121?

Normal Distribution: sample mean, standard error of mean, probability

1. A population of unknown shape has a mean of 75. you select a sample of 40. the standard deviation of the sample is 5. What is the probability that the sample mean is between 76 and 77? a. 0.3980 b. 0.8905 c. 0.0081 d. 0.3943 2. a population has a mean of 50 and a standard deviation of 12. FOr samples of size 9, sam

Calculations based on Normal distribution such as probability in an interval

1 The distribution of purchase amounts of customers of a popular retail store is normal with a mean of $25 and a standard deviation of $8. a. What percentage of customers spends less than $35? b. What percentage of customers spends between $15 and $35? c. Find the dollar amount such that 80% of customers spend at least t

Normal Distribution

Suppose that IQ scores in one region are normally distributed with a standard deviation of 16. Suppose also that exactly 55% of the individuals from this region have IQ scores of greater than 100 (and that 45% do not). What is the mean IQ score for this region? Carry your intermediate computations to at least four decimal plac

Probability of normal distribution

21. A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for Mensa? 23. The time to complete a final examinat

Probability Distributions of normal distribution

3. Delta airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. A. Show the graph of the probability density function for flight time B. What is the probability that the flight

Probability and Sample Mean

The lifetime of a certain brand of batteries are known to be normally distributed with a mean of 1600 hours and a standard deviation of 400 hours. A random sample of 64 of these batteries is taken. What is the probability that the sample mean lifetime is more than 1500 hours?

Statistics : Sampling Distributions and Sample Means

A random sample of size 25 is taken from a normal population having a mean of 80 and a standard deviation of 5. A second random sample of size 36 is taken from a different normal population having a mean of 75 and a standard deviation of 3. Find the probability that the sample mean computed from the 25 measurements will exceed

Inverse Normal Distribution

SAT scores have a mean 500 and a standard deviation of 100 ACT scores have a mean of 18 and a standard deviation of 6. a. If a school accepts the top 10% what is the minimum ACT score and the minimum SAT score. b. If a school accepts the top 20% what is the minimum ACT and SAT score. c.If a school accepts the top 60% wh

Calculation of probability based on normal distribution

Please show all work such as formula commands. The amount of money that a family of four will spend at Kings Island, including the food and souvenirs, is $130 with a standard deviation of $12. Assume that this distribution is normal. 1. Find the probability that a particular family of four selected at random spends between

Normal Probability Distributions

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

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

Business Math

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

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

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

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


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