Exam 6: Continuous Probability Distributions

Exhibit 6-2 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. -Refer to Exhibit 6-2.What is the minimum weight of the middle 95% of the players?

A major credit card company has determined that its customers charge an average of $280 per month on their accounts with a standard deviation of $20. a.What percentage of the customers charges more than $275 per month? b.What percentage of the customers charges less than $243 per month? c.What percentage of the customers charges between $241 and $301.60 per month?

The center of a normal curve is

The uniform probability distribution is used with

The price of a bond is uniformly distributed between $80 and $85. a.What is the probability that the bond price will be at least $83? b.What is the probability that the bond price will be between $81 to $90? c.Determine the expected price of the bond. d.Compute the standard deviation for the bond price.

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.

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 percentage of items will weigh between 6.4 and 8.9 ounces?

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?

The ages of students at a university are normally distributed with a mean of 21.What percentage of the student body is at least 21 years old?

The probability density function for a uniform distribution ranging between 2 and 6 is

The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces. a.What is the probability that a randomly selected item from the production will weigh at least 4.14 ounces? b.What percentage of the items weigh between 4.8 to 5.04 ounces? c.Determine the minimum weight of the heaviest 5% of all items produced. d.If 27,875 of the items of the entire production weigh at least 5.01 ounces,how many items have been produced?

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?

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

Given that Z is a standard normal random variable,what is the probability that Z -2.12?

Exhibit 6-3 Consider the continuous random variable X,which has a uniform distribution over the interval from 20 to 28. -Refer to Exhibit 6-3.The variance of X is approximately

The time between arrivals of customers at the drive-up window of a bank follows an exponential probability distribution with a mean of 10 minutes. a.What is the probability that the arrival time between customers will be 7 minutes or less? b.What is the probability that the arrival time between customers will be between 3 and 7 minutes?

The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6. a.What is the probability that a randomly selected bill will be at least $39.10? b.What percentage of the bills will be less than $16.90? c.What are the minimum and maximum of the middle 95% of the bills? d.If twelve of one day's bills had a value of at least $43.06,how many bills did the restaurant collect on that day?

The monthly earnings of computer programmers are normally distributed with a mean of $4,000.If only 1.7 percent of programmers have monthly incomes of less than $2,834,what is the value of the standard deviation of the monthly earnings of the computer programmers?

The time it takes to hand carve a guitar neck is uniformly distributed between 110 and 190 minutes. a.What is the probability that a guitar neck can be carved between 95 and 165 minutes? b.What is the probability that the guitar neck can be carved between 120 and 200 minutes? c.Determine the expected completion time for carving the guitar neck. d.Compute 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 in 7 minutes or more is