Answered: The time required (in days) to build a…

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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Question

The time required (in days) to build a house
single-family is a random variable which obeys the normal law whose mean is 45 days and the standard deviation 4 days.
a) What is the probability that it will take between 40 and 52 days
to build a single-family house?
b) If the manufacturer grants a reduction of $2000 on
any house that is not delivered in less than 51 days,
what percentage of buyers will be entitled to it?
c) If the manufacturer only wants to grant this reduction
for 0.5% of the houses it builds, what delivery time should it guarantee?

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 + ...

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Step 1: Solution

Let X be time required (in days) to build a house.

The random variable X has normal distribution with mean is 45 days and the standard deviation 4 days.

$X tilde N left parenthesis mu equals 45 comma space sigma equals 4 right parenthesis$

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