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Exam 8: Continuous Probability Distributions

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Question 41

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The exponential density function f(x) :

A) is bell-shaped.
B) is symmetrical.
C) approaches infinity as x approaches zero.
D) approaches zero as x approaches infinity.

E) B) and C)
F) A) and D)

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Question 42

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What is the mean of the standard normal distribution? a.0 b.−1 c.1 d.2

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Question 43

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Given that Z is a standard normal random variable,a negative value (z) on its distribution would indicate:

What proportion of the data from a normal distribution is within two standard deviations from the mean?

We distinguish between discrete and continuous random variables by noting whether the number of possible values is countable or uncountable.

If the random variable X is exponentially distributed with parameter λ = 2,then the probability that X is between 1 and 2 equals the probability that X is between 2 and 3.

What is the median of the standard normal distribution? a.1 b.−1 c.0 (because the distribution is symmetric,mean=median=mode) d.2

Phone Orders The L.L.Bean catalog department that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. -{Phone Orders Narrative} What is the value of λ,the parameter of the exponential distribution in this situation?

The 10th percentile of a Z distribution has 10% of the Z-values lying above it.

If P(t > t_.01,v) = 2.50,then the number of degrees of freedom v is:

Let X represent weekly income expressed in dollars.Since there is no set upper limit,we cannot identify (and thus cannot count)all the possible values.Consequently,weekly income is regarded as a continuous random variable.

What is the mode of the standard normal distribution? a.0 (because the distribution is symmetric,mean=median=mode) b.−1 c.1 d.2

Suppose X has a normal distribution with mean 40 and standard deviation 2.Shifting all the X values to the right 10 units results in a normal distribution with mean ____________________ and standard deviation ____________________.

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

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. ​ ​ -{Battery Life Narrative} What lifetime should the manufacturer advertise for these batteries in order that only 2% of the lamps will wear out before the advertised lifetime?

Counter Sales suppose that customers arrive at a counter at an avarage rate of three customers per minute and their arrivals follow the poisson model. -{Counter Sales Narrative} Use the appropriate exponential distribution to find the probability that the next customer will not arrive within the next 2 minutes.

If X is a continuous random variable on the interval [0,10],then P(X > 5)= P(X ≥ 5).

The shape of an F distribution is ____________________.

Suppose you have a Student t distribution with 20 degrees of freedom. a.Find the mean. b.Find the variance. c.Find the standard deviation.

A normal distribution is symmetric; therefore the probability of being below the mean is 0.50 and the probability of being above the mean is 0.50.