A construction company has taken up a project to build a high-rise office complex inPenang. The time required to complete a construction project is normally distributedwith a mean of 80 weeks and a standard deviation of 10 weeks. A constructioncompany must pay a penalty if the project is not finished by the due date in thecontract.1 (a) If a construction company bidding on this contract puts in a due date of 70weeks, what is the probability that they will have to paya penalty? Your answer shouldbe in four decimal places.

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Answered: A construction company has taken up 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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The Centers for Disease Control report that the total cholesterol levels for women, age 20-29, are normally distributed with a mean of 183 milligrams per deciliter and a standard deviation of 37.2 milligrams per deciliter. If 30 women (age 20-29) were randomly selected what is the probability that the mean total cholesterol level of these 30 women will be less than 200 milligrams per deciliter?
Fast Auto Service provides oil and lube service for cars. It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car and the standard deviation is 2.4 minutes. The management wants to promote the business by guaranteeing a maximum waiting time for its customers. If a customer's car is not serviced within that period, the customer will receive a 50% discount on the charges. The company wants to limit this discount to at most 3% of the customers. What should the maximum guaranteed waiting time be? Assume that the times taken for oil and lube service for all cars have a normal distribution.Round your answer to the nearest minute.
The monthly income of undergraduate students of AZ University is known to follow a normal distribution with a mean of Tk. 9000 and a standard deviation of Tk. 2500. A career bootcamp is being organized to help boost the students' career prospects. The bootcamp curriculum is designed for students who are currently earning between Tk. 7000 and Tk. 12000, therefore only students who meet the requirements will be eligible for the program. a) What is the probability that a randomly selected student earns more than Tk. 10000? b) Determine the 75th percentile income of the students. c) What is the probability that a randomly selected student will not satisfy the requirement for the bootcamp? d) Historically, the bootcamp was seen to most benefit students who were in the top 10.25% of the accepted range. What is the minimum income a participating student can have if they want to get the maximum benefit from the program?
A particular fruit's weights are normally distributed, with a mean of 429 grams and a standard deviation of 13 grams. If you pick one fruit at random, what is the probability that it will weigh between 411 grams and 467 grams > Next Question
A semi-truck can transport a maximum of 14,950 pounds. Suppose that a load of cargo containing 115 boxes needs to be transported via this semi-truck. Research has shown that the weights of boxes for this type of cargo have a distribution that has a population mean weight of 125 pounds and a population standard deviation of 20 pounds. Based on this information, what is the probability that all 115 boxes can be safely loaded into the semi-truck and transported?
Each week a grocer purchases 60 gallons of milk at the beginning of the week. At the endof the week any unused milk must be thrown away. The demand for milk is normally distributed witha mean of 51 gallons per week and a standard deviation of 9 gallons per week. (a) What is the probability that the store runs out of milk at some point during the week? (b) What is the probability that the grocer does not run out of milk in any of the next five weeks?
The time taken in the cycling phase of a triathlon has a mean 23.16min and standard deviation 8.39min. Find the probability that the mean cycling time taken by a random sample of 38 competitors is greater than 25 minutes. Give your answer in 3 decimal places.
11. If the scores for an IQ Test have a mean of 100 and a standard deviation of 15, find the probability of a student having an IQ score that will fall below 112.
Suppose that home prices (in thousands of dollars) in a certain region have a mean of 360 and a standard deviation of 180. A realtor randomly selects a sample of 90 homes in the region. Estimate the probability that the sample mean home price from the realtor's data is greater than 400 (thousand dollars). You must justify your solution, and note any assumptions you are making.
Suppose a college admissions test is normally distributed with a mean of 500 and a standard deviation of 100. If a student scores in the 75th percentile, what is their test score? If the top 10% of test takers are eligible for a scholarship, what is the minimum score needed to qualify for the scholarship? If the test is taken twice by the same student, and the scores are independent, what is the probability that their average score is above 550?
A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 55 miles and a standard deviation of 8 miles. Find the probability of the following events: The car travels between 49 and 63 miles per gallon. Probability =
A company records the mean time in years that used passenger cars and used pick-up trucks were kept before being sold by the owner. The mean time for used car is 5.6 years with a standard deviation of 1.5 years. For pick-up trucks, the mean time is 6.8 years with a standard deviation of 2.2 years. What is the probability that the mean time that 100 pick-up trucks were kept exceeds the mean time that 64 used cars were kept by at least 1.8 years?

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