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Normal Distribution

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

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

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

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

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: 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

Population and Standard Mean

1. Assume the population standard deviation is a=25. (The a is actually the funny looking 0 with the line that goes from the top right up at an angle) Compute the standard error of the mean O (funny o with line) line over x, for sample sizes of 50, 100, 150, and 200. What can you say about the size of the standard error of the m


What is the purpose of developing a frequency distribution? What is the relationship between the relative frequency and the cumulative frequency? Could a frequency distribution contain qualitative data? Why? Describe the properties of a normal distribution. Why are there infinite possible normal distributions? Why should one

Risk Analysis Question

In performing a symmetric approximation, you calculate a mean of the total system cost as $1,725K. The variance is 22500. The POE is $1,600K. What is the probability of overrunning the POE? 50.56% 29.67% 83.33% 79.67%

Weights of Water Taxi Passengers

When a water taxi sank in the Baltimore Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lbs. It was also noted that the mean weight of a passenger was assumed to be 140 lbs. Assume a "worst case" scenario in which all the passengers are adult men. (This could easily occur in a

Finding Area Under the Standard Normal Distribution Curve

1.)The average monthly mortgage payment including principal and interest is $982 in the United States. If the standard deviation is approximately $180 and the mortgage payments are approximately normally distributed, find the probability that a randomly selected monthly payments is: A. More than $1000 B. More than $1475 C. B

Calculating Standard Normal Probability Distribution

Solve the following: 1. Assume that the thermometer readings are normally distributed with a mean of 0° C and a standard deviation of 1.00° C. A thermometer is randomly selected and tested. For each case given below, draw a sketch and find the probability. The given values are in Celsius degrees. [Note: If using a calculator

Normal Modelling of IQ Test Scores

I find this question really difficult to answer and I need help formulating a response. Some IQ tests are standardized to a normal model with a mean of 100 and a standard deviation of 16. a. Draw a model for these IQ scores, clearly label it , showing what the 65-95-99.7 rule predicts about the score. b. In what interv

Normal Distribution Curve/Chart Statistics

I need to know how to solve this question using the normal distribution curve / chart and how to answer using Excels Fx statistics function The first statistics exam had a mean of 65 and a standard deviation of 10 points; the second had a mean of 80 and a standard deviation of 5 points. Derrick scored an 80 on both tests. Jul

Statistics Problem for standard normal distribution

1. The mean amount of gasoline and services charged by Key Refining Company credit customers is $70 per month. The distribution of amounts spent is approximately normal with a standard deviation of $10. What is the probability of selecting a credit card customer at random and finding the customer charged between $70 and $83?

Which choice is another term that can be used to describe a normal distribution?

1)Which choice is another term that can be used to describe a normal distribution: A) discrete distribution B) negatively or positively skewed C) bell curve D) independent variable 2) If a normal distribution has a mean of 30 and a standard deviation of 5, then A) the median is 35 and the mode is 25. B) the median is 30

Discussing the Distribution Theory

1. Let the random variable X have the pdf f(x) = 2/sqrt(2(pi)) e^(-x^2/(2) ), 0<x<infinity, zero elsewhere. Find the mean and the variance of X. Hint: Compute E(X) directly and E(X^2) by comparing the integral with the integral representing the variance of a random variable that is N(0,1). 2. Compute P(X_1 + 2X_2 - 2X

Normal Distribution of diastolic blook pressure readings

Suppose we have set of blood pressure with a mean of 80 Diastolic, and a sample standard deviation of 10 points. If we assume a normal distribution of Diastolic blood pressures, between what two values can we be assured 99.7% of all Diastolic blood pressures will lie?

Statistics: Normal Distribution Cotton Cloth Problem

1. The quality of cotton cloth is a function of the quality of the raw cotton used in its manufacture. One key attribute of raw cotton is the length of the cotton fibers: the longer the better. Suppose a yarn mill buys raw cotton from a cotton gin that produces cotton fiber with a mean length of 1.25 inches and a standard deviat

Interpreting Normal Distributions

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?