Automotive engineers have found that the gas mileage in highwaydriving of a certain sports utility van is normally distributed witha mean of 13.6 kilometers per liter and a standard deviation of1.5 kilometers per liter.Find the probability that a random sample of 16 sports utilityvans has a mean between 13.2 and 14.2 kilometers per liter.O P(-1.07 < Z < 1.60) = 0.1423 – 0.9452O P(1.07 < Z < 1.60) = 0.9452 – 0.8577%D|O P(-1.07 < Z < 1.60) = 0.9452 – 0.8577O P(-1.07 < Z < 1.60) = 0.9452 – 0.1423

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Answered: Automotive engineers have found that…

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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A machine produces glass with a nominal thickness of 4mm. In fact the thickness is a Normal random variable with mean 4.168mm and standard deviation 0.12mm. The thickness in mm which 5% of panes exceed is (2 d.p.)?
Suppose that an airline uses a seat width of 16.7 in. Assume that men have hip breadths that are normally distributed with a mean of 14.2 inches, and a standard deviation of 1in. Find the probability that if an individual man is randomly selected that his hip breadths will be greater than 16.7 in.
An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.7 minutes. A random sample of 36 dive durations has a mean of 12.3 minutes and a standard deviation of 2.1 minutes. At a = 0.01 is there enough evidence to reject the oceanographer's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. (a) Identify the claim and state H, and H, Ho Ha (Type integers or decimals. Do not round.) The claim is the hypothesis.
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An expensive watch is powered by a 3-volt lithium battery expected to last four years. Suppose the life of the battery has a standard deviation of 0.3 year and is normally distributed a. Determine the probability that the watch's battery will last longer than 4.2 years. b. Calculate the probability that the watch's battery will last more than 3.35 years c. Compute the length-of-life value for which 10% of the watch's batteries last longer. Round answers to 4 decimal places
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
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A certain city the Transportation Authority (CTA) has trollies leaving regularly throughout the day beginning at 5:00 a.m. Although the length of a trip and the number of stops are constant, the time taken for each trip varies due to weather, traffic, and time of the day. According to the CTA, the mean time taken for the trip is 50 minutes. Suppose the travel time is Normally distributed with standard deviation o = 4 minutes. A random sample of 25 trips is obtained, and the time for each is recorded. Find the probability that the sample mean time will be less than 48 minutes.
The photoresist thickness of wafers in semiconductor manufacturing has a mean of 10.6 micrometers and a standard deviation of 1.3 micrometers. An engineer takes a sample of 50 wafers once a week and calculates the mean thickness of these wafers. If the mean of this sample is either less than 10.41 micrometers or greater than 10.79 micrometers, the engineer will conclude that the machine needs an adjustment. The probability that, based on a sample of 50 wafers, the engineer will conclude that the machine needs an adjustment is: O 0.6970 O 0.1091 O 0.3030 O 0.2522 O 0.1506
4.2
Given a normally distributed random variable X with a mean of 196 and a standard deviation of 20, find the value of x such that Pr(X < x) = 0.511. (Please round your answer to one decimal place, e.g. 0.6.)

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