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Exam 6: Continuous Probability Distributions

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Question 51

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Exhibit 6-6 The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. -Refer to Exhibit 6-6. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?

A) 0.4772
B) 0.9772
C) 0.0228
D) 0.5000

E) All of the above
F) None of the above

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Question 52

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The average life expectancy of dishwashers produced by a company is 6 years with a standard deviation of 8 months. Assume that the lives of dishwashers are normally distributed. a.What is the probability that a randomly selected dishwasher will have a life expectancy of at least 7 years? b.Dishwashers that fail operating in less than 4years will be replaced free of charge. What percent of dishwashers are expected to be replaced free of charge? c.What are the minimum and the maximum life expectancy of the middle 95% of the dishwashers' lives? Give your answer in months. d.If 155 of this year's dishwasher production fail operating in less than 4 years and 4 months, how many dishwashers were produced this year?

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a.0.0668
b.1.22%
c.5...

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Question 53

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For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is

Exhibit 6-7 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. -Refer to Exhibit 6-7. What is the probability that a randomly selected item will weigh more than 10 ounces?

A random variable X is uniformly distributed between 45 and 150. a.Determine the probability of X = 48. b.What is the probability of X ≤60? c.What is the probability of X ≥50? d.Determine the expected vale of X and its standard deviation.

Exhibit 6-9 The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of $220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed. -Refer to Exhibit 6-9. What is the minimum value of the middle 95% of computer prices?

For a uniform probability density function,

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. -Refer to Exhibit 6-1. The probability density function has what value in the interval between 6 and 10?

The monthly income of residents of Daisy City is normally distributed with a mean of $3000 and a standard deviation of $500. a.The mayor of Daisy City makes $2,250 a month. What percentage of Daisy City's residents has incomes that are more than the mayor's? b.Individuals with incomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes? c.What are the minimum and the maximum incomes of the middle 95% of the residents? d.Two hundred residents have incomes of at least $4,440 per month. What is the population of Daisy City?

The average starting salary of this year's MBA students is $35,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. What are the minimum and the maximum starting salaries of the middle 95% of MBA graduates?

The time it takes a worker on an assembly line to complete a task is exponentially distributed with a mean of 8 minutes. a.What is the probability density function for the time it takes to complete the task? b.What is the probability that it will take a worker less than 4 minutes to complete the task? c.What is the probability that it will take a worker between 6 and 10 minutes to complete the task?

The SAT scores of students are normally distributed with a mean of 950 and a standard deviation of 200. a.Nancy Bright's SAT score was 1390. What percentage of students have scores more than Nancy Bright? b.What percentage of students score between 1100 and 1200? c.What are the minimum and the maximum values of the middle 87.4% of the scores? d.There were 165 students who scored above 1432. How many students took the SAT?

Z is a standard normal random variable. What is the value of Z if the area between -Z and Z is 0.754?

For a standard normal distribution, determine the probability of obtaining a Z value of a.greater than zero. b.between -2.34 to -2.55 c.less than 1.86. d.between -1.95 to 2.7. e. between 1.5 to 2.75.

A negative value of Z indicates that

Exhibit 6-6 The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. -Refer to Exhibit 6-6. What percentage of MBA's will have starting salaries of $34,000 to $46,000?

An exponential probability distribution

The weights of the contents of cans of tomato sauce produced by a company are normally distributed with a mean of 8 ounces and a standard deviation of 0.2 ounces. a.What percentage of all cans produced contain more than 8.4 ounces of tomato paste? b.What percentage of all cans produced contain less than 7.8 ounces? c.What percentage of cans contains between 7.4 and 8.2 ounces? d.Ninety-five percent of cans will contain at least how many ounces? e. What percentage of cans contains between 8.2 and 8.4 ounces?

A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation.

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. -Refer to Exhibit 6-1. The probability of assembling the product between 7 to 9 minutes is