Ch. 6 Stats

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

C) 0.10

Find the probability P 1.96 Z 1.96).

C) 0.9500

What can be said about the expected value and standard deviation of an exponential distribution?

The expected value is equal to the standard deviation.

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.

0.0000

Let the time between two consecutive arrivals at a grocery store checkout line be exponentially distributed with a mean of three minutes. Find the probability that the next arrival does not occur until at least four minutes have passed since the last arrival.

0.2636

Suppose that the probability that a continuously measured X is below 3 is P(X<3)=F(3)=45%, while the probability that X is below 1 is P(X<1)=F(1)=5%. What is the probability that X is between 1 and 3, P(1<X<3):

All above is true

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?

All of the above.

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.

When attending a movie, patrons are interested in avoiding the pre-movie trivia games, ads, and previews. It is known that the previews begin at the scheduled movie start time and they last between 5 and 15 minutes. Assume that the time of the previews is uniformly distributed. The expected time of the pre movie ads and the probability that on a given day the previews last more than 12 minutes are

10, 0.3

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

Let X be normally distributed with mean μ = 250 and standard deviation σ = 80. Find the value x such that P(X ≤ x) = 0.0606.

126

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

2

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?

C) 0.1765

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 = 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).

(What is CDF?) 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.

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

f(x) is symmetric around the mean.

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 beendecided 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?

B) 54,900

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 is characterized by uncountable values and can take on any value within an interval.

TRUE

Patients scheduled to see their primary care physician at a particular hospital wait, on average, an additional eight minutes after their appointment is scheduled to start. Assume the time that patients wait is exponentially distributed. What is the probability a randomly selected patient will have to wait more than 10 minutes?

0.2865

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

0.5

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 P(c≤X≤d)=d−c/b−a.

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?

0.8092

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

If an exponential distribution has the rate parameter λ = 5, what is its variance?

1/25

If an exponential distribution has the rate parameter λ = 5, what is its expected value?

1/5

Patients scheduled to see their primary care physician at a particular hospital wait, on 11) average, an additional eight minutes after their appointment is scheduled to start.Assume the time that patients wait is exponentially distributed. What is the probability a randomly selected patient will see the doctor within five minutes of the scheduled time?

D) 0.4647

We are often interested in finding the probability that a continuous random variable assumes a particular value.

FALSE