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Exam 8: Continuous Probability Distributions

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Question 31

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A continuous probability distribution represents a random variable having an infinite number of outcomes that may assume any number of values within an interval.

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Question 32

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Let z₁ be a z-score that is unknown but identifiable by position and area. If the symmetrical area between -z₁ and + z₁ is 0.9544, the value of z₁ is 2.0.

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Question 33

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If the z-value for a given value x of the random variable X is z = 2.326, and the distribution of X is normal with a mean of 50 and a standard deviation of 5, to what x-value does this z-value correspond? $\begin{array}{|l|l|}\hline\text { A. } & 11.63 . \\\hline \text { B. } & 61.63 . \\\hline \text { C. } & 63.16 . \\\hline \text { D. } & 16.31 . \\\hline\end{array}$

In the normal distribution, the flatter the curve, the larger the standard deviation

The mean and standard deviation of an exponential random variable cannot equal to each other.

Given that Z is a standard normal variable, the variance of Z: $\begin{array}{|l|l|}\hline A&\text { is always greater than 2.0 .}\\\hline B&\text {is always greater than 1.0 . }\\\hline C&\text { is always equal to 1.0 .}\\\hline D&\text { cannot assume a specific value.}\\\hline \end{array}$

If the random variable X is normally distributed with a mean of 75 and a standard deviation of 8, then P(X ≤ 75) is: $\begin{array}{|l|l|}\hline \text { A. } & 0.125 . \\\hline \text { B. } & 0.975 . \\\hline \text { C. } & 0.625 \\\hline \text { D. } & 0.500 \\\hline\end{array}$

If the random variable X is normally distributed with a mean of 70 and a standard deviation of 10, find the following values of the distribution of X. a. First quartile. b. Third quartile.

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 $\ge$ 5). c. P(X $\le$ 8).

The mean and the standard deviation of an exponential distribution are equal to each other.

A random variable X is normally distributed with a mean of 250 and a standard deviation of 50. Given that X = 175, its corresponding z-score is -1.50.

Which of the following is true for a normal distribution? $\begin{array}{|l|l|}\hline A&\text {It is unimodal. }\\\hline B&\text {It is symmetrical. }\\\hline C&\text {It has a bell shape. }\\\hline D&\text {All of these choices are correct. }\\\hline \end{array}$

What are the values of z that correspond to the P(-z $\le$ Z $\le$ z) equal to 0.4778? $\begin{array}{|l|l|}\hline A&\pm 0.2389\\\hline B&\pm 0.71\\\hline C&\pm 0.64 \\\hline D&\text { None of these choices are correct.}\\\hline \end{array}$

Which of the following distributions is suitable to model the length of time that elapses before the first telephone call is received by a switchboard? $\begin{array}{|l|l|}\hline\text { A. } & \text { Exponential. } \\\hline \text { B. } & \text { Normal. } \\\hline \text { C. } & \text { Poisson. } \\\hline \text { D. } & \text { Uni form. } \\\hline\end{array}$

Which of the following distributions is not symmetrical? $\begin{array}{|l|l|}\hline\text { A. } & \text { Exponential } \\\hline \text { B. } & \text { Uni form. } \\\hline \text { C. } & \text { Normal. } \\\hline \text { D. } & \text { None of these choices are correct. } \\\hline\end{array}$

Continuous probability distributions describe probabilities associated with random variables that are able to assume any of an infinite number of values.

Given that Z is a standard normal random variable, the area to the left of a value z is expressed as: $\begin{array}{|l|l|}\hline\text { A. } & P(Z \geq z) \\\hline \text { B. } & P(Z \leq z) \\\hline \text { C. } & P(0 \leq Z \leq z) \\\hline \text { D. } & P(Z \geq-z) \\\hline\end{array}$

In the normal distribution, the mean, median and mode are all at the same position on the horizontal axis since the distribution is symmetric.

If the continuous random variable X is uniformly distributed over the interval [15, 25], then the mean of X is: $\begin{array}{|l|l|}\hline\text { A. } & 40 \\\hline \text { B. } & 25 \\\hline \text { C. } & 20 \\\hline \text { D. } & 15 . \\\hline\end{array}$

Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.8212? $\begin{array}{|l|l|}\hline \text { A. } & 0.92 . \\\hline \text { B. } & -0.05 . \\\hline \text { C. } & 0.05 . \\\hline \text { D. } & -0.92 . \\\hline\end{array}$