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# Normal Distribution

### Standard Deviations and the Empirical Rule

The VIX is quoted in terms of percentage points and translates, roughly, to the expected movement in the S&P 500 index over the next 30-day period, on an annualized basis. For example, if the VIX is at 21, this represents an expected annualized change of 21% over the next 30 days; thus one can infer that the index option ma

### Normal Probability: Standard Normal Distribution

Question: A set of 50 data values has a mean of 40 and a variance of 25. I. Find the standard score (z) for a data value = 47. II. Find the probability of a data value > 47. III. Find the probability of a data value < 47. Show all work.

### Percentage of automobiles are exceeding the speed limit - Findle

The speed limit on Interstate 75 around Findlay, Ohio, is 65 mph. On a clear day with no construction, the mean speed of automobiles was measured at 63 mph with a standard deviation of 8 mph. If the speeds are normally distributed, what percentage of the automobiles are exceeding the speed limit? If the Highway Patrol decides to

### Normal Distribution

Assume that the average annual salary for a worker in the United States is \$30,500 and that the annual salaries for Americans are normally distributed with a standard deviation equal to \$6,250. Find the following: (A) What percentage of Americans earn below \$19,000? (B) What percentage of Americans earn above \$40,000?

### Symmetric Property of Normal Distribution

An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is known to be normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. Between what two values (in ounces) symmetrically distributed a

### Probability of computer performance score above 200

Assume that Performance Scores are normally distributed. What is the probability that a randomly selected notebook PC would have a performance score above 200? mean=183.47 Standandard deviation=29.115 x=200 Standard z-score= x-Âµ ------- ? =

### Probability of average length of aluminum-coated steel sheets

Please solve the exercise in Excel and show your work (including formulas) The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.27 inches. A sample of 9 metal sheets is randomly selected from a batch. What is the probability that the a

### Find Percentage from Normal Distribution

Calculate the % of a 9-inning MLB games resulting in 5 or fewer hits. An analysis was done to study the odds of # of hits in MLB for all 9 inning MLB Games played b/w 1960-2005. The distribution of hits/9-inning is approximately normal w/mean of 7.52 & std of 1.10.

### Probability of a sample average number of strokes exceeding

Please answer the exercise below in Excel and show your work including formulas. A PGA (Professional Golf Association) tournament organizer is attempting to determine whether hole (pin) placement has a significant impact on the average number of strokes for the 13th hole on a given golf course. Historically, the pin has been

### Statistics: Price-to-earnings ratio distribution; sample audit of customer accounts

Select the correct answer and explain briefly why: 11. The price-to-earnings ratio for firms in a given industry is distributed according to normal distribution. In this industry, a firm with a standard normal variable value of Z=1: A. Has an average price-to-earnings ratio B. Has a below average price-to-earnings ratio C

### OurCampus! Statistics for Managers Using Excel

See attached files. To Satisfy concerns of potential advertisers, the management of OurCampus! has undertaken a research project to learn the amount of time it takes users to download a complex video features page. The marketing department has collected data and has made some claims based on the assertion that the data follo

### Statistics Practice Questions

Please select the correct answer (please write in a few words how you have a arrived at your conclusion) 12. In a statistic class, 10 scores were randomly selected with the following results were obtained (mean=71.5): 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the standard deviation? A. 22.72 B. 12.00 C. 4.77 D. 5

### Use z table to calculate standard normal probability

Use the table of standard normal probabilities (z table) to answer the following questions. What is P(z > 0.5)? What is P(-0.8 < z < 1.5)? What is P(z < -1.2)? What z-value leaves 95 % of the normal distribution to its right? What z-value, and its negative, leaves 20 % of the normal distribution in each ta

### Overdue Bills Following a Normal Curve & Determining Likely Voters

6. A large population of overdue bills has balances that follow a normal curve. When we take a sample of 100 of these the average is \$500 and the SD is \$100. (a) What statement can you make about the range \$300 to \$700? (b) What statement can you make about the range \$480 to \$520? 10. Pollsters try to determine wh

### Normal Distribution and Probability: Average of the Sample

A business finds the average cost required to complete a project is \$416 with a standard deviation of \$57. A sample of 36 project cost reports was selected at random. Assuming that the distribution of the costs is normal, what is the probability that the average for this sample is between \$400 and \$425?

### Computing order point: Example operations analyst

Bob Billy is an operations analyst for Dollar-Does-It stores based in Iva, SC. Â He is currently studying the order and stocking policies for a top-selling toy. Â His analysis has indicated an almost constant lead time of 10 days. Â Bob calculated that the daily demand was normally distributed with a mean of 1,250 toys per day w

### Define the Normal Distribution and Describe its Properties

What is a normal distribution? Describe the properties of a normal distribution. Please provide references.

### Properties of a Normal Distribution

Describe the properties of a normal distribution. Explain why there are an infinite number of normal distributions. Why do you want to assume that your sample data represent a population distribution?

### Standard Deviation Determination

Calculate the Standard Deviation of your data. USING EXCEL. THESE ARE MY NUMBERS 26 19 21 15 23 22 18 24 16 19 Is this a normal distribution? What are the implications? The following items will be assessed in particular: Your ability to describe a normal distribution as evi

### Determining Variables from Mean, and Standard Deviation of Data

Suppose the weight of a typical American male follows a normal distribution with mean=180 lb and standard deviation=30 lb. Also, suppose 91.92% of all American males weigh more than I weigh. a. What fraction of American males weigh more than 225 pounds? b. How much do I weigh?

### The lifetimes of light bulbs of a particular type are normally distributed.

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of the bulbs have lifetimes that lie within one standard deviation of the mean on either side? Use the 68-95.99.7 Rule. Please give a through and simplistic explanation in th

### Normal Probability Explained for Final Exam Grades

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 8. Only 5% of the students taking the test scored higher than what grade?

### Normal dist: Empirical rule &Circle graph & Measurement scale

1) Using the empirical rule, determine the approximate percentage of a normal distribution that is expected to fall within 1 standard deviation of the mean. A. 34% B. 50% C. 47.5 % D. 68% 2) A department of mathematical sciences has majors in four areas Major Number of Majors Mathematics

### Price range for contractor to build home for middle 80% markets

If the average price of a new home is 145,500 find the max and min prices of homes the contractor would build to attract the middle 80% of the market. Assume that the standard deviation is 1,500 and the variable is normally distributed.

### Frequency Distribution and Data Samples

I have several questions relate to frequency distribution that I need support. Please see my questions below and please post with examples if you can so I have more understanding. 1. Does it necessarily true that any frequency distribution contains any form of data sample? Please illustrate your answer with examples. 2. C

### Standard Deviation and Standard Error for Disease Y study

Consider that measurement 2 (M2) in a random sample of 1000 controls from the Disease Y study population follows the normal distribution. The sample mean of M2 is 90 and 95% of the sample observation falls within 70 and 110. Calculate the sample standard deviation and standard error of the sample mean and intepret. I would

### Business: Decision Justifications Using Z-score And Statistics

Assume that you own a small factory. A critical piece of machinery in your factory will need to be replaced in 180 days. If the machinery does not show up on time, you will need to shut down until it arrives. This might cause you to permanently lose customers.When you order the part you will need to pay the \$500,000 in advance.

### Proving the standard normal distribution has zero skew and kurtosis

** Please see attached file for the complete problem description ** Prove that the standard normal distribution (mean 0, standard deviation 1) has zero skew and kurtosis (4th moment divided by standard deviation to the 4th power) equal to 3. (please see the attached file)

### Graph and calculate standard normal distribution of formula

See attachment for the formula. I need to graph the standard normal distribution by using the formula provided. Where pi is approximately 3.14 and e is approximately 2.718. Use X values of -2, -1.5, -1, -0.05, 0, 0.05, 1, 1.5 and 2. Use a calculator to compute the Y values. In the attachment F(x) is y in the textbook.

### Standard normal distribution

1. Ages of applicants for a particular scholarship are normally distributed with a mean age of 21.3 years and a standard deviation of 1.85 years. If an applicant is randomly selected, find the probability that the applicant is under 18 years old. Express answer as a decimal - four decimal places. 2. Song lengths scheduled fo