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Exam 8: Continuous Probability Distributions

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Question 31

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

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Question 32

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

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Question 33

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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).

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

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? $\begin{array}{|l|l|}\hline \text { A. } & 0.92 . \\\hline \text { B. } & -0.05 . \\\hline \text { C. } & 0.05 . \\\hline \text { D. } & -0.92 . \\\hline\end{array}$

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

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 70 and a standard deviation of 10, find the following values of the distribution of X. a. First quartile. b. Third quartile.

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? $\begin{array}{|l|l|}\hline\text { A. } & \text { Exponential. } \\\hline \text { B. } & \text { Normal. } \\\hline \text { C. } & \text { Poisson. } \\\hline \text { D. } & \text { Uni form. } \\\hline\end{array}$

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

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.

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.

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

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

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

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

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

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

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

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? $\begin{array}{|l|l|}\hline\text { A. } & 11.63 . \\\hline \text { B. } & 61.63 . \\\hline \text { C. } & 63.16 . \\\hline \text { D. } & 16.31 . \\\hline\end{array}$