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Normal Distribution

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

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

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

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

Assessing Sampling distributions

1. Find the area under the standard normal curve to the left of z = 1.93. 2. A traffic study at one point on an interstate highway shows that vehicle speeds are normally distributed with a mean of 61.3 mph and a standard deviation of 3.3 mph. If a vehicle is randomly checked, find the probability that its speed is between 55.

14 multiple choice statistics problems.

1. What type of statistical comparison can be made when observed statistics are proportions and the sample size is greater than 30? a. t-test b. z-test c. ANOVA d. f-test 2. With a normal distribution, we know that a. Approximately 95% of all observations will fall with

Calculations with Normal Distributions

3.6-16 If the moment-generating function of X is M(t) = e^(500t+5000t^2), find P[27,060 (less than or equal to) (X-500)^2 (less than equal to) 50,240] 3.6-17 If X is N(7,4), find P[15.364 (less than or equal to) (X-7)^2 (less than or equal to) 20.096]. 3.6-18 The strength X of a certain material is such that its distributi

Business problem using statistics

* Please see attachment* i am submitting a complex lengthy stats problem, with accompanying excel file. I am beginning stats student. I am more interested in theoretical explanations to help me to learn the problem. I am also interested in basic level internet references to help me to understand material. It is irrelevant