QM 235 Chapter 6 Test

The starting salary of an administrative assistant is normally distributed with a mean of $50,000 and a standard deviation of $2,500. We know that the probability of a randomly selected administrative assistant making a salary between μ - x and μ + x is 0.7416. Find the salary range referred to in this statement.

$47,175 to $52,825

The probability P(Z < -1.28) is closest to _______.

0.10

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider must wait between 1 minute and 1.5 minutes?

0.1765

Find the probability P(-1.96 ≤ Z ≤ 0).

0.4750

Let X be normally distributed with mean μ and standard deviation σ > 0. Which of the following is true about the z value corresponding to a given x value?

-The z value corresponding to x = μ is zero. -A positive z = (x - μ)/σ indicates how many standard deviations x is above μ. -A negative z = (x - μ)/σ indicates how many standard deviations x is below μ. Answer is all of the above.

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take exactly 3.7 hours to construct a soapbox derby car.

0.000

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take more than five hours to construct a soapbox derby car.

0.0228

Suppose the life of a particular brand of laptop battery is normally distributed with a mean of 8 hours and a standard deviation of 0.6 hours. What is the probability that the battery will last more than 9 hours before running out of power?

0.0475

Gold miners in Alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1,000 tons of dirt is normally distributed. What is the probability the miners find more than 16 ounces of gold in the next 1,000 tons of dirt excavated?

0.0918

The probability P(Z > 1.28) is closest to _______.

0.10

A superstar major league baseball player just signed a new deal that pays him a record amount of money. The star has driven in an average of 110 runs over the course of his career, with a standard deviation of 31 runs. An average player at his position drives in 80 runs. What is the probability the superstar bats in fewer runs than an average player next year? Assume the number of runs batted in is normally distributed.

0.1660

Suppose the round-trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between Boston and San Francisco will be more than $450?

0.1788

For any normally distributed random variable with mean μ and standard deviation σ, the proportion of the observations that fall outside the interval [μ - σ, μ + σ] is the closest to _________.

0.3174

Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bound of $3.50 per gallon and an upper bound of $3.80 per gallon. What is the probability a randomly chosen gas station charges more than $3.70 per gallon?

0.3333

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take between 2.5 and 3.5 hours to construct a soapbox derby car.

0.3830

Gold miners in Alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1,000 tons of dirt is normally distributed. What is the probability the miners find between 10 and 14 ounces of gold in the next 1,000 tons of dirt excavated?

0.4972

The probability that a normal random variable is less than its mean is _______.

0.5

Suppose the round-trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between Boston and San Francisco will be between $325 and $425?

0.5274

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider waits less than two minutes?

0.5294

The time for a professor to grade a student's homework in statistics is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes. What is the probability that randomly selected homework will require between 11 and 15 minutes to grade?

0.5704

The time for a professor to grade a homework in statistics is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes. What is the probability that randomly selected homework will require more than 12 minutes to grade?

0.5948

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider must wait more than 1.5 minutes?

0.6471

Alex is in a hurry to get to work and is rushing to catch the bus. She knows that the bus arrives every six minutes during rush hour, but does not know the exact times the bus is due. She realizes that from the time she arrives at the stop, the amount of time that she will have to wait follows a uniform distribution with a lower bound of 0 minutes and an upper bound of six minutes. What is the probability that she will have to wait more than two minutes?

0.6667

You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. An inexpensive bag you are considering advertises to be good for temperatures down to 38°F. What is the probability that the bag will not be warm enough?

0.7734

You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. One sleeping bag you are considering advertises that it is good for temperatures down to 25°F. What is the probability that this bag will be warm enough on a randomly selected May night at the park?

0.8106

The time for a professor to grade a student's homework in statistics is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes. What is the probability that randomly selected homework will require less than 16 minutes to grade?

0.9131

Find the probability P(-1.96 ≤ Z ≤ 1.96).

0.9500

The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is _______.

1/(b - a) between a and b, and zero otherwise.

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. Find the mean and standard deviation of the waiting time.

115 seconds and 49.07 seconds

You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. Above what temperature must the sleeping bag be suited such that the temperature will be too cold only 5% of the time?

18.84

How many parameters are needed to fully describe any normal distribution?

2

A hedge fund returns on average 26% per year with a standard deviation of 12%. Using the empirical rule, approximate the probability the fund returns over 50% next year.

2.5%

A daily mail is delivered to your house between 1:00 p.m. and 5:00 p.m. Assume delivery times follow the continuous uniform distribution. Determine the percentage of mail deliveries that are made after 4:00 p.m.

25%

Let X be normally distributed with mean µ = 25 and standard deviation σ = 5. Find the value x such that P(X ≥ x) = 0.1736.

29.70

Let X be normally distributed with mean µ = 250 and standard deviation σ = 80. Find the value x such that P(X ≤ x) = 0.9394.

374

An investment consultant tells her client that the probability of making a positive return with her suggested portfolio is 0.90. What is the risk, measured by standard deviation that this investment manager has assumed in her calculation if it is known that returns from her suggested portfolio are normally distributed with a mean of 6%?

4.69%

Sarah's portfolio has an expected annual return at 8%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has an approximate _______.

50% chance that the actual return will be greater than 8%

The salary of teachers in a particular school district is normally distributed with a mean of $50,000 and a standard deviation of $2,500. Due to budget limitations, it has been decided that the teachers who are in the top 2.5% of the salaries would not get a raise. What is the salary level that divides the teachers into one group that gets a raise and one that doesn't?

54,900

The time of a call to a technical support line is uniformly distributed between 2 and 10 minutes. What are the mean and variance of this distribution?

6 minutes and 5.3333 (minutes)2

The stock price of a particular asset has a mean and standard deviation of $58.50 and $8.25, respectively. Use the normal distribution to compute the 95th percentile of this stock price.

72.07

Gold miners in Alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1,000 tons of dirt is normally distributed. If the miners excavated 1,000 tons of dirt, how little gold must they have found such that they find that amount or less only 15% of the time?

8.88

For any normally distributed random variable with mean μ and standard deviation σ, the percent of the observations that fall between [μ - 2σ, μ + 2σ] is the closest to _______.

95.44%

You work in marketing for a company that produces work boots. Quality control has sent you a memo detailing the length of time before the boots wear out under heavy use. They find that the boots wear out in an average of 208 days, but the exact amount of time varies, following a normal distribution with a standard deviation of 14 days. For an upcoming ad campaign, you need to know the percent of the pairs that last longer than six months—that is, 180 days. Use the empirical rule to approximate this percent.

97.5%

The cumulative distribution function is denoted and defined as which of the following?

F(x) and F(x) = P(X ≤ x)

A continuous random variable has the uniform distribution on the interval [a, b] if its probability density function f(x) _______.

Is constant for all x between a and b, and 0 otherwise.

If X has a normal distribution with µ = 100 and σ = 5, then the probability P(90 ≤ X ≤ 95) can be expressed in terms of a standard normal variable Z as _______.

P(-2 ≤ Z ≤ -1)

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X < 20) related to P(X < 16)?

P(X < 20) is greater than P(X < 16).

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X > 16) related to P(X < 16)?

P(X > 16) is greater than P(X < 16).

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X > 24) related to P(X < 16)?

P(X > 24) is the same as P(X < 16).

It is known that the length of a certain product X is normally distributed with μ = 20 inches and σ = 4 inches. How is the probability P(X > 28) related to P(X < 16)?

P(X > 28) is smaller than (X < 16).

The cumulative distribution function F(x) of a continuous random variable X with the probability density function f(x) is which of the following?

The area under f over all values that are x or less.

Which of the following does not represent a continuous random variable?

The number of customer arrivals to a bank between 10 am and 11 am.

What does it mean when we say that the tails of the normal curve are asymptotic to the x axis?

The tails get closer and closer to the x axis but never touch it.

Which of the following is not a characteristic of a probability density function f(x)?

f(x) is symmetric around the mean.

Find the z value such that P(Z ≤ z) = 0.9082.

z = 1.33

Find the z value such that P(-z ≤ Z ≤ z) = 0.95.

z = 1.96