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# Normal Distribution

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### Statistics: Normal distribution for eye surgical procedure

A health care analyst would like to know that if the duration of a given eye surgical procedure has a normal distribution with a mean of 240 minutes and a standard deviation of 40 minutes, what percent of procedures of this type lasts between 220 and 260 minutes?

### Z scores

6.18 Many manufacturing processes use the term work-in-process (often abbreviated as WIP). In a book manufacturing plant, the WIP represents the time it takes for sheets from a press to be folded, gathered, sewn, tipped on end sheets, and bound. The following data (stored in the file wip.xls) represent samples of 20 books at eac

### Statistics binonmial distribution: probability of success of 0.5

Consider a binomial distribution with 15 identical trials, and a probability of success of 0.5 i. Find the probability that x = 2 using the binomial tables ii. Use the normal approximation to find the probability that x = 2. Show all work

### Statistics Practice Test: 7 questions about sixth graders

See attached files. Download the file entitled "elementary.xls." This file contains data on the 100 6th grade students at Oceanview Elementary School in Wichita, Kansas. Use this data to answer the questions below. Unless otherwise noted, use the 5% confidence level for all calculations. 1. Describing the Data a) Ident

### Mileage Probabilities

Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made a study of the maintenance costs and determined the number of miles traveled during the year followed the normal distribution. The mean of the distribution was 60,000 miles and the standard deviation 2,000 miles. a. What percent of the Ford S

### Jolt Electrical Supply Normal distribution

It has been observed that electrical connectors manufactured by Jolt Electrical Supply Company last an average of 18.2 months and follow a normal distribution with a standard deviation of 1.7 months. Jolt agrees to replace any connector that fails within 19 months. Out of 500 connectors sold, how many does Jolt expect to repla

### Statistics: Normal distributions, real estate data for Denver, Colorage (See data file attached).

See data file attached. Refer to the attached real estate data, which report information on homes sold in the Denver, Colorado, area during the last year. a. The mean selling price (in \$ thousands) of the homes was computed earlier to e \$221.10 with a standard deviation of \$47.11. Use the normal distribution to estimate t

### Commuting Time for Average Resident for East Coast

The average resident of a certain East Coast suburb spends 42 minutes per day commuting, with a standard deviation of 12 minutes. Assume a normal distribution. Find the percent of all residents of this suburb who have the following commuting times. At least 50 minutes per day Between 32 and 40 minutes per day

### Breaking strength of packing ropes

The breaking strength of packing ropes are normally distributed, with a mean of 5 pounds per square inch and a standard deviation of 1.5 pounds per square inch. What proportion of the ropes has a breaking strength between 5 and 6.5 pounds?

### Maximum Likelihood Estimation

Let the random samples x1, x2, x3,... xn drawn from normal distribution with known mean zero a. Construct the likelihood function b. Find the Nature Log of the likelihood function c. Find the best estimate of the variance by MLE d. What is the relationship between this estimate and the second moment <x²> e. If we use seco

### Normal distributions: Probabilities and percentiles

The highway police in a certain state are using aerial surveillance to control speeding on a highway with a posted speed limit of 55 miles per hour. Police officers watch cars from helicopters above a straight segment of this highway that has large marks painted on the pavement at 1-mile intervals. After the police officers obse

### Stochastic Inventory Model: An Example

A bagel shop buys each bagel for .08 and sells each bagel for .35. Leftover bagels at the end of they day are purchased by a local soup kitchen for .03 per bagel. The shop owner has observed daily demand (Q), the following probabilities (F(Q) Q=0, F(Q)= .05 Q=5, F(Q)= .1 Q= 10 F(Q)= .1 Q= 15, F(Q)= .2 Q= 20, F(Q)= .25

### Distribution of IQ scores and standard deviation

1.) Test one: mean is 80 and standard deviation is 9. Mark scores 91 Test two: mean is 77 and standard deviation is 6. Mark score 87 Find the percentile for all Which test Mark did better? Why? 2.) What is the the standard deviation for IQ tests? If someone's IQ is 140, how many standard deviation is it above the

### Statistics-Check whether sample drawn from Normal Population

Ques: a) Check whether the following sample has been drawn from a Normal population. b) Calculate 95% Confidence interval for population Variance and standard deviation. 26.7, 25.8, 24.0, 24.9, 26.4, 25.9, 24.4, 21.7, 24.1, 25.9, 27.3, 26.9, 27.3, 24.8, 23.6

### Activity Estimation Constructions

Suppose the following estimates of activities (in weeks) for the construction of a swimming pool were provided, along with their immediate predecessors. What is the probability that the project will be completed within 21 weeks? Within 22 weeks? Activity A B C D

### Estimating Mean Percent Change in Population

1. Bone loss by nursing mothers. Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in mineral content of the spines of 47 mothers during three months of breast-feeding. Here are the data: -4.7

### Six Sigma Computation and Interpretations

To what probabilities do each of the following sigma levels correspond to, based on a standard normal curve: 3 sigma, 4sigma, 5 sigma, and 6 sigma? (Hint: Use the NORMSDIST function in Excel. Note that this function returns the standard normal cumulative distribution function. The distribution has a mean of 0 (zero) and a standa

### Normal Distribution and Probability

Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per decili

### Life tests on sample of five units were conducted to evaluate design

17.1 Life tests on a sample of five units were conducted to evaluate a component design before release to production. The units failed at the following times: Unit Failure Time, Number hours 1 1200 2 1900 3 2800 4 3500 5 4500 Suppose

### Paired Difference Test

A paired difference experiment produced the following results a) Determine the values of z for which the null hypothesis, m1 -m2 = 0, would be rejected in favor of the alternative hypothesis, m1 - m2 < 0. Use a = 0.10 b) Conduct the paired difference test described in part a. Draw the appropriate conclusions. c) What assump

### Advanced probability and Statistics

1.Suppose a normal distribution has u =1.4,and o =0.2, calculate the z -score f or x= 3.5 2.What is the mode of the data set 23, 44, 22, 23, 23, 44, 23, 55? 3. Give the following data set 50, 40, 33, 37, 60 a. Find the mean, median and mode b. Find the standard deviation

### Normally distributed - Population Mean & SD

1. Assume that each energy type is produced by a process that is normally distributed and calculate the population mean and SD from the entire data set (1980 -2005). 2. Determine the probability that next year's production will exceed production in 1990 for each type. Year Coal 2 Natural Gas 3 Crude Oil 4 Nuclear Electric

### Case Study

Practice Problem: At the age of 42 Enrique Chavez was starting thinking more and more about retirement. After 17 years of running one of the bay area's tattoo parlor he decided to take on a partner - his 21 year old bilingual niece Diana. Her words still echoed in his head - the same words she repeated every time someone left h

### Normally Distributed: A light bulb manufacturer claims her bulbs have a population mean life of 1,000 hours. Is this claim justified at the ...

A light bulb manufacturer claims her bulbs have a population mean life of 1,000 hours. Is this claim justified at the .05 level if a random sample of 25 bulbs has a sample mean of 994 hours with a standard deviation of 30 hours? Assume the population life expectancy of the bulbs is normally distributed.

### Normal distribution: Word problems

An aptitude test is designed to measure leadership abilities of the test subjects. Suppose that the scores on the test are normally distributed with a mean of 580 and a standard deviation of 120. The individuals who exceed 780 on this test are considered to be potential leaders. What proportion of the population are considered t

### Normal distribution raw scores

Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, portfolio managers give a questionnaire to new customers to measure their desire to take financial risks. The scores on the questionnaire are approximately normally distributed with a mean of 49.5 and a sta

### Frequency Numbers for Data Representations

The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.00 and use a class width of 0.20. Does the frequency distribution appear to be roughly a normal distribution? 0.39 0 0 0.29 0 0.54 0 0.17 0 0 1.25 0 0.16 0 0.02 0 0.21 0 0.13 0.46 0

### Mean and Normal Distribution

A machine cuts plastic into sheets that are 30 feet (360 inches) long. Assume that the population of lengths is normally distributed. a) The company wants to estimate the mean length the machine is cutting the plastic within 0.25 inch. Determine the minimum sample size required to construct a 90% confidence interval or the

### What is the standard error of the mean in this experiment?

The Oil Price Information Center reports the mean price per gallon of regular gasoline is \$3.26 with a population standard deviation of \$0.18. Assume a random sample of 40 gasoline stations is selected and their mean cost for regular gasoline is computed. a. What is the standard error of the mean in this experiment? b. Wha

### Percentile of a Normal Probability Distribution

A vending machine dispenses coffee into a twelve ounce cup. The amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.08 ounce. You can allow the cup to overfill 10% of the time. What amount should you set as the mean amount of coffee to be dispensed? = ? ounces