Exam 6: Continuous Probability Distributions

The records show that 8% of the items produced by a machine do not meet the specifications. Use the normal approximation to the binomial distribution to answer the following questions. What is the probability that a sample of 100 units contains a.Five or more defective units? b.Ten or fewer defective units? c.Eleven or less defective units?

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?

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. -Refer to Exhibit 6-1. The standard deviation of assembly time (in minutes) is approximately

For a standard normal distribution, the probability of z 0 is

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

The First National Mortgage Company has noted that 6% of its customers pay their mortgage payments after the due date. a.What is the probability that in a random sample of 150 customers 7 will be late on their payments? b.What is the probability that in a random sample of 150 customers at least 10 will be late on their payments?

Z is a standard normal random variable. The P (1.41 < Z < 2.85) equals

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?

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

The average life expectancy of computers produced by Ahmadi, Inc. is 6 years with a standard deviation of 10 months. Assume that the lives of computers are normally distributed. Suggestion: For this problem, convert ALL of the units to months. a.What is the probability that a randomly selected computer will have a life expectancy of at least 7 years? b.Computers that fail in less than 5 years will be replaced free of charge. What percentage of computers are expected to be replaced free of charge? c.What are the minimum and the maximum life expectancy of the middle 95% of the computers' lives? Give your answers in months and do not round your answers. d.The company is expecting that only 104 of this year's production will fail in less than 3 years and 8 months. How many computers were produced this year?

Exhibit 6-5 The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. -Refer to Exhibit 6-5. The probability that her trip will take exactly 50 minutes is

Exhibit 6-8 The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. -Refer to Exhibit 6-8. What is the probability that a randomly selected tire will have a life of exactly 47,500 miles?

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.119?

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 price of a stock is uniformly distributed between $30 and $40. a.What is the probability that the stock price will be more than $37? b.What is the probability that the stock price will be less than or equal to $32? c.What is the probability that the stock price will be between $34 and $38? d.Determine the expected price of the stock. e.Determine the standard deviation for the stock price.

Given that Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1401?

The weekly earnings of bus drivers are normally distributed with a mean of $395. If only 1.1 percent of the bus drivers have a weekly income of more than $429.35, what is the value of the standard deviation of the weekly earnings of the bus drivers?

The length of time it takes students to complete a statistics examination is uniformly distributed and varies between 40 and 60 minutes. a.Find the mathematical expression for the probability density function. b.Compute the probability that a student will take between 45 and 50 minutes to complete the examination. c.Compute the probability that a student will take no more than 40 minutes to complete the examination. d.What is the expected amount of time it takes a student to complete the examination? e.What is the variance for the amount of time it takes a student to complete the examination?

X is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that X equals 19.62 is

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. If 513 of the MNM computers were priced at or below $647.80, how many computers were produced by MNM?