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Exam 6: Continuous Probability Distributions

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Question 51

Multiple Choice

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A continuous random variable may assume

A) all values in an interval or collection of intervals
B) only integer values in an interval or collection of intervals
C) only fractional values in an interval or collection of intervals
D) all the positive integer values in an interval

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Question 52

Multiple Choice

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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 she will finish her trip in 80 minutes or less is

A) 0.02
B) 0.8
C) 0.2
D) 1.00

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Question 53

Multiple Choice

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If the mean of a normal distribution is negative,

For a continuous random variable x, the probability density function fx) represents

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 between 11 and 12 ounces?

For the standard normal probability distribution, the area to the left of the mean is

The random variable x is known to be uniformly distributed between 70 and 90. The probability of x having a value between 80 to 95 is

For a normal distribution, a negative value of z indicates

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?

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 $47,500?

An airline has determined that 20% of its international flights are not on time. Use the normal approximation to the binomial distribution to answer the following questions. What is the probability that of the next 80 international flights a. Fifteen or less will not be on time? b. Eighteen or more will not be on time? c. Exactly 17 will not be on time?

The Globe Fishery packs shrimp that weigh more than 1.91 ounces each in packages marked" large" and shrimp that weigh less than 0.47 ounces each into packages marked "small"; the remainder are packed in "medium" size packages. If a day's catch showed that 19.77 percent of the shrimp were large and 6.06 percent were small, determine the mean and the standard deviation for the shrimp weights. Assume that the shrimps' weights are normally distributed.

The ticket sales for events held at the new civic center are believed to be normally distributed with a mean of 12,000 and a standard deviation of 1,000. a. What is the probability of selling more than 10,000 tickets? b. What is the probability of selling between 9,500 and 11,000 tickets? c. What is the probability of selling more than 13,500 tickets?

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

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 at least 30,000 miles?

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 probability that a randomly selected computer will have a price of at least $1,530?

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

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?

X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that X is less than 9.7 is

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 probability density function has what value in the interval between 20 and 28?