The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.04 flawsper square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel.(a) What is the probability that there are no surface flaws in an auto's interior?(b) If 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws?(c) If 10 cars are sold to a rental company, what is the probability that at most 1 car has any surface flaws?Round your answers to four decimal places (e.g. 98.7654).(a) The probability is i!(b) The probability is i!(c) The probability is i

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The lengths of lumber a machine cuts are normally distributed with a mean of 97 inches and a standard deviation of 0.5 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 97.18 inches? (b) A sample of 43 boards is randomly selected. What is the probability that their mean length is greater than 97.18 inches?
The lengths of lumber a machine cuts are normally distributed with a mean of 86 inches and a standard deviation of 0.6 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 86.21 inches? (b) A sample of 41 boards is randomly selected. What is the probability that their mean length is greater than 86.21 inches?
A study by the American Heart Association studied the distribution of birth weights for 1295 newborns (preterm babies excluded). They found that the birth weight of human babies is approximately normally distributed with a mean of 7.6 pounds and a standard deviation of 1.09 pounds. (a.) What is the probability that a randomly chosen baby weighs more than 9 pounds at birth? (b.) What is the probability that a randomly chosen baby weights between 6 and 8 pounds at birth? (c.) What is the 80th percentile for birth weight?
6) Assume that the heights of men are normally distributed with a mean of 68.0 inches and a standard deviation of 3.5 inches. If 100 men are randomly selected, find the probability that they have a mean height greater than 69 inches.
The average fuel efficiency of U.S. light vehicles (cars, SUVs, minivans, vans, and light trucks) for 2005 was 21 miles per gallon (mpg). If the standard deviation of the population was 2.8 and the gas ratings were normally distributed, (a) what is the probability that the mean mpg for a random sample of 25 light vehicles is under 18? (b) between 20 and 24?
The height of American women is believed to follow a normal distribution with mean μ = 5.38 feet and standard deviation σ = 0.2083 feet. (b) A study randomly selects 30 American women. What is the probability that the mean height of women in this sample is greater than 5.5 feet? (c) Another study randomly selects 50 American women. Will there be a lower or higher probability that the mean height of the 50 women in this sample is greater than 5.5 feet, compared to the study in part (b)? Explain. (d) Instead, for which of the two studies from parts (b) and (c) there is a higher probability that the mean height of the women in the sample is between 5.33 and 5.43 feet? Explain.
A research team is working on a project to study the time (in seconds) for high school male runners to finish a 400-meter race. Jimmy, a junior researcher in the team, has randomly selected a sample of 25 male runners from a high school and the time (in seconds) for each of them to complete a 400-meter race was recorded. The sample mean running time was 53 seconds. It is assumed that the running time in a 400-meter race follows a normal distribution with a population standard deviation of 5.5 seconds.(a) Give a point estimate of the population mean running time for a 400-meter race.(b) Calculate the sampling error at 95% confidence level.(c) Construct a 95% confidence interval estimate of the population mean running time for a 400-meter race.
The lengths of lumber a machine cuts are normally distributed with a mean of 90 inches and a standard deviation of 0.4 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 90.12 inches? (b) A sample of 39 boards is randomly selected. What is the probability that their mean length is greater than 90.12 inches?
The amountof cashew nuts per packet (?), sold by a company,can be modelled usinga normal random variable with a mean of 115.0 grams and a varianceof 4.0 grams. Determine the probability that the amount of cashew nuts, in a randomly selected packetsold by this company,is: (a)more than 113grams; (b)between 117.5grams and 120grams.
A manufacturer knows that their items have a normally distributed length, with a mean of 10 inches, and standard deviation of 3.2 inches.If 3 items are chosen at random, what is the probability that their mean length is less than 12.2 inches?
The lengths of lumber a machine cuts are normally distributed with a mean of 100 inches and a standard deviation of 0.4 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 100.16 inches? (b) A sample of 41 boards is randomly selected. What is the probability that their mean length is greater than 100.16 inches?
Suppose the number of hours of sleep a person gets per night follows a normal distribution with a mean of 7 hours and a standard deviation of 1.5 hours. What is the probability that a randomly selected person gets between 6 and 8.5 hours of sleep per night? If the top 10% of people who get the most sleep are considered "long sleepers," what is the minimum number of hours of sleep per night required to be a long sleeper?

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