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Normal Distribution

Normal distribution

A very large number of fish are swimming in a lake. Their weights are normally distributed with mean 1.30kg and a standard deviation 0.40kg. Fish caught with weights less than 0.5kg have to be thrown back. a) If an angler catches a randomly selected fish, what is the probability that the fish has to be thrown back? b) find

Normal distribution

A university professor keeps records of his travel time while he is driving between his home and the university. Over a long period of time he has found that his morning travel times are approx Normally distributed with a mean of 31 minutes and a standard deviation of 3.0 minutes;his return journey in the evening is similarly d

Joint Distributions (normal distributions)

Tim has two more problems to solve on his test, but he doesn't know how long it will take to finish them. He assigns mutually irrelevant normal distributions to the times, assigning a mean of 35 minutes to the first problem and 30 minutes to the second problem. He assigns a 95% chance that the first problem will take 35+-15 minu

Normal distribution and percentiles

True or false: It is not possible for the score in a distribution, not necessarily normal, which ranks as the 90th percentile to also be the mode for the distribution.

Normal Distribution

In a production run of 40 of a particular model of radiation detector, there are four which have defective circuits. If a sample of three of these is chosen without replacement, what is the probability that all three will be defective?

Normal distribution, standard deviation and mean

True or false: When the variable is normally distributed, the sample size is less than 30, and the population standard deviation is known, then the t distribution must be used to find confidence intervals for the mean.

Normal Distribution

VISA reported with 95% confidence that 19% of those surveyed used checks to pay for purchases. If 1478 people participated in the survey, what was the percentage of error?

Normal Distribution

A tornado has blown through a section of Collinsville. The insurance adjuster wants to estimate the average claim to within $500. If the standard deviation is believed to be $1600 and the company wants to be 99% sure of their figures, how large a sample must be taken?

Normal distribution and significance levels

True or false: A retailer wants to estimate with 99% confidence the number of people who buy at his store. A previous study showed that 15% of those interviewed had shopped at his store. He wishes to be accurate within 3% of the true proportion. The minimum sample size necessary would be 940.

Normal distribution, standard deviation and mean

If IQ scores on a Stanford-Binet Test are normally distributed with a mean of 100 and a standard deviation of 15, then about how many people in a randomly chosen million would be expected to score at 160 or above? (This was at one time the break off score for the "genius" designation.) a) 47 b) 32 c) 16

Normal Distribution

#2 If you are grading the class according to your z score in a normal distribution. would you rather have a score of 70 in class A where the mean is 55 and the standard deviation is 10, or a score of 80 in class B where the mean is 60 and standard deviation is 15? What would the percentile rank be in class A and B and what does

Normal Approximation

Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) Answers to different questions are independant. Jodi is a good student for whom

Monthly income and expense plan for the Terrels

Donna and Sherman Terrel are preparing a budget for 2003. Donna is a systems analyst with an airplane manufacturer, and Sherman is working on a master's degree in educational psychology. The Terrels do not have any children or other dependents. Donna estimates her salary will be about $36,000 in 2003; Sherman expects to work onl

Probability, normal distribution

An airline company knows that over the long run, only 90% of passengers who reserve seats show up for their flight. On a flight with 300 seats, the airline accepts 324 reservations. Assume the passengers show up independently. 1. Give the upper bound on the probability that the flight will be overbooked (more than 300 peop

Determining the sampling distribution of a proportion.

According to a well-known newspaper journal, 58.3% of the 222,900 households in a particular county get the Sunday edition of the local newspaper. Suppose that random samples of 200 households are selected. In what proportion of the samples will between 55% and 60% of the households get the Sunday edition of the newspaper?

Working with inference.

What is the difference in the average daily hotel room rates between Minneapolis and New Orleans? Suppose we want to estimate this difference by taking hotel rate samples from each city and using a 98% confidence level. The data for such a study follows. Use this data to produce an interval estimate and also a point estimat

Normal Distribution. Suppose that the height of a man is normally distributed with a mean of 5'9" (69") and a standard deviation of 2". Find the minimum height of the ceiling of an airplane, such that at most 2% of the men walking down the aisle will have to duck their heads?

Suppose that the height of a man is normally distributed with a mean of 5'9" (69") and a standard deviation of 2". Find the minimum height of the ceiling of an airplane, such that at most 2% of the men walking down the aisle will have to duck their heads? A. Define the random variable? B. List the parameters for the distribut

Standard deviation

Please use MINITAB to solve or explain how I can use MINITAB to solve. 7. Assume that the midterm's scores X are normally distributed. Let X have a mean of 72 and a standard deviation of 12. Then answer the following three questions: a. What is the probability of obtaining a score at least 90? b. What is the probabil

Family incomes in two particular neighborhoods follow a normal distribution.

QUESTION: Example: Family incomes in two particular neighborhoods follow a normal distribution. For Neighborhood 1 the mean is $26,500, with a standard deviation of $15,000. For Neighborhood 2, the mean is $30,000 with a standard deviation of $18,000. A) What proportion of families in Neighborhood 1 have incomes below the

Normal Distribution

Scores on a college admissions exam are normally distributed with mean score 642 and standard deviation 76. The college wants to set the passing score so that only the best 10% of all applicants pass. what is the passing score?