Answered: ) The mean time for an Auto repair shop…

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 mean time for an Auto repair shop to change the oil in a car is ? = 16.4 minutes with a standard deviation of ? = 3.6

What is the probability that the mean time it takes for sixteen randomly selected oil change jobs, is at most 17 minutes? State your answer to four significance figures.

The slowest 20% of times to change the oil in an automobile is at least what time? State your answer to the nearest tenth of a minute.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

The probability that the mean time it takes for sixteen randomly selected oil change jobs at most 17 minutes is obtained below:

From the given information, a population of values has a normal distribution with mean 16.4 and standard deviation of 3.6 and sample of size n = 16.

Here,

The required formula is given below:

The required value is given below:

Thus, the probability that the mean time it takes for sixteen randomly selected oil angel jobs at most 17 minutes is 0.8665.

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