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Normal Distribution

Normally and Non-Normally Distributed Population

The majority of the data is normally distributed if there are enough subjects. For instance, if you collected test scores of only a few honor students, the data will most likely not be normally distributed because you would have a sample that did not represent the entire population. But the identical test scores (for honor stude

Continuous Probabilities: Normal Distributions

Task Background: In this week's discussion, you learned how to construct probability distributions and graph them. This week, you will review continuous probabilities, more specifically normal distributions. You are hired as a statistical analyst for Silver's Gym, and your boss wants to examine the relationship between body f

Normal Distributions and Curves

(a) Answer true or false to each of the following statements (i) Two normal distributions that have the same mean are centered at the same place, regardless of the relationship between their standard deviations. (ii) Two normal distributions that have the same standard deviation have the same shape, regardless of the relatio

Normal Distribution using Excel

I would like the response to sample problems below in excel format. 6.48 An orange juice producer buys all his oranges from a large orange grove. The amount of juice squeezed from each of these oranges is approximately normally distributed, with a mean of 4.70 ounces and a standard deviation of 0.40 ounce. A. What is the

Soft-drink volume in test

A soft-drink bottler sells "one-liter" bottles of ginger ale. The production manager wishes to monitor the content of the bottles. He takes a random sample of 30 bottles, and obtains the following contents, in milliliters: 1025 977 1018 975 977 990 959 957 1031 964 986 914 1010 988 1028 989 1001 984 974 1017 1060 1030 991

Statistical Analysis: Normal Distribution

See the attached file. Using the Coins Generator feature in the Data menu of the statdisk software, available at, 100 sets of 30 coin tosses were simulated, and the observed number of heads was recorded for each of the 100 trials. The sorted results for the observed number of heads appear below. 8 9 10

Gasoline, grocery stores, and the Better Business Bureau

1. The average price of a gallon of unleaded regular gasoline was reported to be $2.34 in northern Kentucky. Use this price as the population mean, and assume the population standard deviation is $0.20. a. What is the probability that the mean price for a sample of 30 service stations is within $0.03 of the population mean?

Sampling Distributions in Tennessee Grilled Pork

As the manager of Tennessee Grilled Pork, you have been aslned to examine the company's national employment data and perform a follow-up study on the duration of employment for Tennessee Grilled Pork's employees. You have been asked to study a random sample of 144 former employees. Assume that the population of all employed i

Mean height of males aged 18 - 24

According to the U.S. National Center for Health Statistics, the mean height of 18 -24 year old American males is = 69.7 inches. Assume the heights are normally distributed with a standard deviation of 2.7. Fill in the following blanks: a. About 68.26% of 18 -24 year old American males are between __ and __ inc

Statistics: Distribution Analysis

54. A family is considering a move from a midwestern city to a city in California. The distribution of housing costs where the family currently lives is normal, with mean $105,000 and standard deviation $18,200. The distribution of housing costs in the California city is normal with mean $235,000 and standard deviation $30,400.

Turning browsers into buyers

Sample question: One of the biggest issues facing e-retailers is the ability to turn browsers into buyers. This is measured by the conversion rate, the percentage of browsers who buy something in their visit to a site. The conversion rate for a company's website was 10.1%. The website at the company was redesigned in an attempt

Business Statistics Question Sheet

6) Does the data seem closer to being normal (empirical rule) or not? Use your answers from problems 1-5 above to explain. 7) Your employer, Woodbridge Electric Inc., wants to offer a warranty on the new compact fluorescent light bulb that they have produced and tested. You are called into a meeting and operational experts p

Calculating the indicated probability values

Assume that x has a normal distribution with specified mean and standard deviation. Find the indicated probabilities. a. P(14< x <18), mu = 12, sigma= 1.3____________ b. P(X>120), mu= 116, sigma= 4.7____________ c. P(x<206), mu= 192, sigma= 4.8____________

Normal Distributions and Confidence Intervals

1. Five machines produce electronic components. The number of components produced per hour is normally distributed with a mean of 25 and a standard deviation of 4. a. What percentage of the time does a machine produce more than 27 components per hour? b. What percentage of the time is the average rate of output of the five ma

Hypothesis Testing Using Normal Distribution

Use the given claim to state a null and an alternative hypothesis. Identify which hypothesis represents the claim. A. Claim: p < 0.205 B. Claim: p > 0.70 Test the claim about the population mean µ with a z-test using the given sample statistics and l

Normal distribution bell curve

So, what is the Normal Distribution, and when you think you know what it is, post a real-example of one (other than height), then ask yourself is it really normally distributed? Can everything be normally distributed, that is, fall along a 'bell curve'?

Using Probability in Business Analysis

See the attachments. I. Complete the frequency table found in the Excel spreadsheet attachment. (see attached) II. Using the data found on the OnlyTheBestDiamonds tab in FinalData.xlsx Excel spreadsheet, find the mean, median, mode and standard deviation for the: a. metal value (1 = sterling silver, 2 = gold, 3 = platin

Statistics: Determining Normal Distribution

Operations and production managers often use the normal distribution as a probability model to forecast demand in order to determine inventory levels, manage the supply chain, control production and service processes, and perform quality assurance checks on products and services. The information gained from such statistical anal

Analyzing Water Sample Data with Minitab

I have several questions about water samples that I am having difficulty with. Please utilize minitab to complete work. 1. Fifty samples of water effluent from a chemical processing facility were measured for a required EPA report. The ppm of suspended solids in each specimen is presented in the following table. (a) Examine

DJIA: Market Capitalization and Distribution

Thirty companies comprise the DJIA. Just how big are these companies? One common method for measuring the size of a company is to use its market capitalization, which is computed by multiplying the number of stock shares by the price of a share of stocks. On June 19, 2009, the market capitalization of these companies ranged from

Linear Statistical Models - True or False

Question 2 Decide if the following statements are true or false. Justify your answers. a) If X and Y are two random variables with zero coefficient of correlation then X and Y are independent. b) If X and Y are independent random variables, then their coeflicient of correlation is zero. c) Let X and Y be two random

Mean Annual Household Consumption

Estimate the mean annual amount spent on household consumption per family with a sample of 100 families, an average amount of $8,000 spent, and if the population standard deviation is $500, For a 80% confidence level, z=1.282. The confidence interval estimate of the population mean annual amount spent is 7935.92 to 8064.08.

Statistics Problem: Young Adult Drug Use

The results of the 2009 Survey on Drug Use and Health found that among young adults ages 18-25, in the last month, 22.8% had used marijuana; 2.4% had used cocaine; 3.8% had abused prescription drugs. If we select 500 young adults at random, approximate the probability of the given event. a. Less than 10 had abused prescription

Standard Normal Distribution Function

Let Phi(x) be the cumulative distribution function in the standard normal distribution. a) Use L'Hopital's rule to show that the limit as x goes to - infinity of xPhi(x) equals 0. b) Show that sign [(d/dx)(Phi(x)/Phi'(x))] = sign (Phi'(x) + Phi(x)x). c) Use (a) and (b) to show that Phi(x)/Phi'(x) is increasing in x ove

Sampling Distribution and Test Proportion

Use the following information for problems 1-3. Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance using the given sample statistics. 1. Claim: p > 0:30; = 0:05. Sample statistics: p^ = 0:35, n = 50. 2. Claim

Statistics Problem: Interference

Suppose Z and V are two independent random variables, Z has the normal distribution with expected value 0 and variance 1 and V = 1 or -1, each with probability 0.5. Let Y = ZV. a. Derive the distribution of Y. b. Find the covariance of Y and Z. c. Are Y and Z independent? Justify your answer.

Statistics Problem: Effective Manufacturing Adjustments

The data in the attachment provides two random samples from two successive days runs of a product. You adjusted the manufacturing process after the first day in an attempt to decrease the mean value. Using interval estimates, to a 95% confidence level, was your most recent adjustment effective?

Statistics: Normal Distribution Question

Hi, I need an explanation on how to solve this? I really do not understand these concepts. Question: The average customer waiting time at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager installs a new system and checks if the use of the new system will decrease av

Statistics: The Normal Distribution and Standard Deviation

Below are questions regarding the weight of football players in the NFL. I need assistance in figuring out the following questions. 1. The weight of football players in the NFL is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. What is the probability that a randomly selected football