The sale price of a certain model of grand pianoacross the country is approximately normallydistributed with a mean of $81,000 and a standarddeviation of $3,900.a) What is the probability of a grand piano selling formore than $82,200.37904b) Consider a set of 20 grand pianos. What is theprobability that 5 or less of the pianos sell for morethan $82,200?0.16927✓c) As these pianos sell across the country, what is theprobability that the first piano that sells for morethan $82,200 is the third piano?0.14615

b ) Probability = 0.169273Explanation:Step 1: Step 2: Step 3: Step 4:

Answered: The sale price of a certain model of…

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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1. The average number of acres burned by forest and range fires in a large New Mexico county is 4,255 acres per year, with a standard deviation of 744 acres. The distribution of the number of acres burned is normal. a.) What is the probability that between 2,540 and 4,190 acres will be burned in any given year? b.)What number of burnt acres corresponds to the 38th percentile?
The length of the long-distance calls made by the employees of a certain company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.5 minutes. Find the probability that a call will last between 5 and 10 minutes. A. .3897 B. .1788. C. .6290. D. .6308
e) Suppose that weekly household expenditures on petrol are normally distributed, with a mean of $120 and a standard deviation of $50. i. A family is randomly selected. Find the probability that this family spends more than $245 per week on petrol? A 2.5 B 0.0062 C 0.9938 D 0.0202 ii. The government wants to promote public transport and will award a prize to the families who spend the lowest amount on petrol. If the government only wants to give a prize to 10% of households, what is the most that a family is allowed to spend on petrol each week to obtain the prize? A $56 B $184 C $3.50 D $217.60 In a sample of 25 families, what is the probability that the average weekly expenditure on petrol will be less than $105? ii. A 0.0668 B 0.9332 C 0.3821 D 0.6179
An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 115 cm and a standard deviation of 5.5 cm. A. Find the probability that one selected subcomponent is longer than 117 cm. Probability = B. Find the probability that if 4 subcomponents are randomly selected, their mean length exceeds 117 cm. Probability = C. Find the probability that if 4 are randomly selected, all 4 have lengths that exceed 117 cm. Probability =
6. Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.11 oz. a. Find the probability that a single can of Coke has at least 12.19 oz. b. Find the probability that a pack of 36 cans of Coke have a mean of at least 12.19 oz. c. Suppose you measured the cans of a random 36-pack and got a sample mean of 12.19 oz. Is it reasonable to assume that the actual population mean is 12.00 oz? Why or why not?
4. The amount of time between taking a pain reliever and getting relief is normally distributed with a mean of 25 minutes and a standard deviation of 3 minutes. Find the probability that the time between taking the medication and getting relief is as follows. a. At least 30 minutes b. At most 20 minutes 5. All incoming freshmen at a major university are given a mathematics diagnosti exam. The scores are normally distributed with a mean of 120 and a standa deviation of 25. If a student scores less than a certain score, he or she will have undergo an intervention program. Find the cutoff score at which 64% of the stude would have to undergo the intervention program. 2021.04.10 09:47
According to AAA, the price of a gallon of regular, unleaded gas across gas stations in Ohio is normally distributed with a mean of $2.39 and a standard deviation of $0.15. If you randomly pick a gas station, what is the probability the price is exactly $2.46 per gallon? A) 0.14 B) 0 C) 1 D) 0.68
Assume that the sales of Teri’s Specialty Cakes has historically followed a normal distribution, with an average of 250 cakes per month, and a standard deviation of 15 cakes.a. What is the probability that the sales for cakes will be no more than 285 over the next month?b. What is the probability that the sales for the cakes will be no more than 230 cakes over the next month?c. What is the probability that the sales for the cakes will be between 245 and 265 over the next month?d. What number of cake demand can Teri reasonably assume with a confidence level of 95%?For a, b, c, and d, please write out your work for at least one of these problems. For all problems, explain your answers and sketch a plot (similar to the handouts and text).

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