а.The management of a national automobile manufacturer advertises afree transmission if the transmission on your new car fails. Theexpects that after this guarantee is offered, the mileage on the transmissions willbe normally distributed with a mean of 65,000 miles and a standard deviation of2,146 miles. If management wants to give free transmission replacements toat most one percent of its automobile purchasers, at what mileage should thewarranty state a free replacement?management

The question is about normal distribution Given : Popl. mean of mileage on the transmission ( μ ) =…

Answered: а. The management of a national…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Sarah and her fiancé are planning for their wedding. Distribution of the number of guests coming to the party is normal with the mean 100 and the standard deviation 10. They need to determine how many guests to book for food from a caterer. The caterer makes the following charges: $50 for each guest that is booked in advance; $90 for each guest who is not booked in advance but shows up on the wedding day. The caterer does not offer any refund even if some booked guests may not show up. Questions: What is the optimal number of guests to book in advance? How much Sarah can save by booking the optimal quantity from a) in advance? What is the expected number of guests that will come to their wedding? If Sarah and her fiancé book 90 guests in advance with the caterer, what is the probability of stock out? If Sarah and her fiancé book 100 guests in advance with the caterer, what is the expected number of meals to be wasted?
1. IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160. Convert Einstein's IQ score to a z score. a. b. If we consider "usual IQ scores to be those that convert z scores between -2 and 2, is Einstein's IQ usual or unusual? C. The organization MENSA, which calls itself the "high IQ society", requires a score of 130 or higher. What percent of adults would qualify for membership? 2. In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 5.4 and a standard deviation of 2.2. Find the probability that a randomly selected study participant's response was: a. Less than 4 b. Between 4 and 6 c. More than 8 3. The red blood cell count for a population of adult males can be approximated by a normal distribution, with a mean of 5.4 million cells…
Activity 2: Toby's Trucking Company determined that the distance traveled per truck per year is normally distributed, with a mean of 50 thousand miles and a standard deviation of 12 thousand miles. a. What would be your conclusion if the proportion of trucks travelled between 34 and 50 thousand miles in a year? b. How many miles will be traveled by at least 80% of the trucks? c. How many miles will be traveled by over 40% of the trucks? d. What are your answers to (b) through (c) if the standard deviation is 10 thousand miles?
1. The position number w(letter) tells us where in the alphabet the given letter is located. For instance: w("b") = 2. Find the mean, median and population standard deviation for the vowel position numbers in the English alphabet.
An insurance company wants to make sure that its best customers (those with lowest value of insurance claims) stay with the company. To achieve this goal, the company plans to offer a 10% discount on the annual health insurance premium for customers with the lowest 20% of annual health care expenses. If the average annual health care expenses for a family of four is $3,650 with a standard deviation of $975, what is the amount of the maximum annual health care expense that will qualify for the proposed discount?
When students use the bus from their dorms, they have an average commute time of 8.263 minutes with standard deviation 2.9321 minutes. Approximately 75.67% of students reported a commute time greater than how many minutes? Assume the distribution is approximately normal. Question 10 options: 1) 6.22 2) 2.28 3) 14.24 4) 10.3 5) We do not have enough information to calculate the value.
. A process that cuts lengths of metal with high precision has historically produced metal rods with length that is normally distributed and with a mean of 800 millimetres (mm). Management at the factory is concerned that after an overhaul of the machine the mean length of the rods being produced could differ from the required 800 mm. If it is found that the rods are not being produced to specifications then the machine will have to be stopped for readjustment, with a consequent loss of production. The production line manager tasked with investigating the issue finds that a (random) sample of 25 rods yielded a mean length of 806 mm and a sample standard deviation of 10 mm. i. The mean of the sample is clearly not the required 800 mm. Say why this is not enough information in itself to say if the machine is operating correctly or not. ii. State the null and alternative hypotheses for this situation.
Consider the following service system. The average inter-arrival time is 10 minutes, and the standard deviation of the inter-arrival time is 10 minutes. The average processing time is 5 minutes with the standard deviation of the processing time being 6 minutes. What is the value of Iq? What is the value of I?
1. Suppose the weight of a dog breed is approximately normally distributed, with a mean of 75 pounds and a standard deviation of 2.4 pounds. Use the empirical rule to answer question one through five. Using the empirical rule, fill in the blanks: а. 68% of the weights will be between and _% of the weights will be between and 79.8 pounds _% of the weights will be between and b. The empirical rule can only be used when c. What percent of dogs weigh less than 77.4 pounds? d. What percent of dogs weigh more than 72.6 pounds? e. What percent of dogs weigh less than 70.2 pounds?. f. Using appropriate methods find what percent of the dogs will weigh between 68 and 81 Ibs.
The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $80 and a standard deviation of $21 . If the management wants to give free gifts to at most 11.7% of the customers, what should the amount be above which a customer would receive a free gift?
1

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