The Christmas bonus amounts for members of a certain credit union are normally distributed with amean of $2000 and a standard deviation of $400. If one of these members was chosen at random:a) Find the probability that the bonus will be less than $1850.b) What percentage of members would have a bonus of more than $1850.c) What is the probability that the bonus will be between $1700 and $2240.d)20% of members also qualify for a Christmas hamper if their bonus is less than a certainamount. What is this amount?

Answered: Image /qna-images/answer/17ccfc95-2bce-4b79-bcbf-2327109d819b.jpg

Answered: The Christmas bonus amounts for members…

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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9.) The mean starting salary for teachers is $53,475 nationally. The standard deviation is approximately $5,250. Assume that the starting salary is normally distributed. a.) State the random variable. b.) Find the probability that a starting teacher will make more than $60,000. c.) Find the probability that a starting teacher will make less than $50,000. d.) Find the probability that a starting teacher will make between $52,000 and $59,500. e.) If a teacher made more than $61,000, would you think the teacher was overpaid? Why or why not?
A waiterbelieves the distribution of his tips has a model that is slightly skewed to the left, with a mean of $8.60 and a standard deviation of $4.20. He usually waits on about 50 parties over a weekend of work. a) Estimate the probability that he will earn at least $450. b) How much does he earn on the best 5% of such weekends?
D. The mean annual cost to attend a attend a college is $44,324. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,590. Ninety percent of all students pay less than what amount?
Suppose that the average loan taken out by small-sized businesses from a commercial bank is $275,000. If the loan sizes are normally distributed with a standard deviation of $25,000, find each of the following: A. The probability that a small-sized business takes out a loan of more than $325,000. B. The probability that a small-sized business takes out a loan between $245,000 & $310,000.
In the study about the family income and their expenditures, families can save an average amount of $2, 010 per month with a standard deviation of $580. If 50 families are randomly selected, what is the probability that the average saving amount per month is lower than $2,000? A) 35.27% B 64.73% C) 45.22% D) 54.78%
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?
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
According to a certain website, the average daily time spent on social networking by internet users worldwide is 145 minutes. Assume the standard deviation is 45 minutes and that the probability distribution is normal. What is the probability that a randomly selected person spends daily at least 3 hours on social networking? Select one: a. 0.7794 O b. 0.2206 c. 0.7823 O d. 0.2177
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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