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Exam 8: Continuous Probability Distributions

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Question 21

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The mean and standard deviation of a normally distributed random variable that has been standardised are one and zero, respectively.

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Question 22

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Given that X is a normal variable, which of the following statements is (are) true?

A) The variable X + 5 is also normally distributed.
B) The variable X - 5 is also normally distributed.
C) The variable 5X is also normally distributed.
D) All of these choices are correct.

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Question 23

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The probability density function f(x) for a uniform random variable X defined over the interval [1, 11] is:

For a normal curve, if the mean is 20 minutes and the standard deviation is 5 minutes, the area to the right of 13 minutes is 0.9192.

In a shopping centre, the waiting time for an elevator is found to be uniformly distributed between 1 and 5 minutes. a. What is the probability density function for this uniform distribution? b. What is the probability of waiting no more than 3 minutes? c. What is the probability that the elevator arrives in the first 30 seconds? d. What is the probability of a waiting time between 2 and 3 minutes? e. What is the expected waiting time?

If the random variable X is exponentially distributed, then which of the following statements best describes the mean of X?

Given that z is a standard normal random variable, a negative value of z indicates that the standard deviation of z is negative.

Which of the following is always true for all probability density functions of continuous random variables?

The expected value, E(X) , of a uniform random variable X defined over the interval $a \leq x \leq b$ , is:

If the random variable X is normally distributed with a mean of 75 and a standard deviation of 8, then P(X ≤ 75) is:

If the random variable X is uniformly distributed over the interval 10 $\leq$ x $\leq$ 50, find the following probabilities. a. $P ( X \geq 30 )$ b. $P ( X \leq 25 )$ c. $P ( 18 \leq X \leq 35 )$ d. $P ( X = 40 )$

Which of the following is not true for a random variable X that is uniformly distributed over the interval $a \leq x \leq b$ ?

Given that Z is a standard normal random variable, the area to the left of a value z is expressed as:

Given that Z is a standard normal random variable, the mean of Z is:

The probability density function, f(x) , for any continuous random variable X, represents:

In the normal distribution, the total area under the curve is equal to one.

Which of the following distributions is not symmetrical?

Consider a binomial random variable X with n = 300 and p = 0.02. Approximate the values of the following probabilities. a. P(X = 4). b. P(X  5). c. P(X  8).

Find the following probabilities: a. $P ( X \leq 1 )$ b. $P ( X \geq 2 )$ c. $P ( 1 \leq X \leq 2 )$ d. $P ( X = 3 )$

Using the standard normal curve, the probability or area between z = -1.28 and z = 1.28 is 0.1003