Question 1

Using the standard normal curve, the area between z = 0 and z = 3.50 is about 0.50.

Accepted Answer

A) True 
 B)False

Question 2

If the random variable X is exponentially distributed with $\lambda$ = 2 parameter, then the variance of the distribution is 0.5.

Accepted Answer

A) True 
 B)False

Question 3

If X is a normal random variable with a mean of 78 and a standard deviation of 5, find the following probabilities:
a. P(X$\le$ 87).
b. P(X $\ge$ 91).
c. P($\le$ X $\le$ ).

Accepted Answer

a. 0.9641.

Question 4

If Z is a standard normal random variable, find the value z for which:
a. P(0 $\leq$ Z $\leq$ z) = 0.276.
b. P(Z $\geq$ z) = 0.341.
c. P(Z $\geq$ z) = 0.819.
d. P(-z $\leq$ Z $\leq$ z) = 0.785.
e. P(Z $\leq$ z) = 0.9279.

Accepted Answer

a. 0.76.
b

Question 5

Which of the following is a characteristic of a normal distribution? $\begin{array}{|l|l|}
\hline  A&\text {It is a symmetrical distribution. }\
\hline  B&\text {The mean is always zero. }\
\hline  C&\text {The mean, median and mode are all equal. }\
\hline  D&\text { All of these choices are correct.}\
\hline 
\end{array}$

Accepted Answer

The answer of Which of the following is a characteristic...

Question 6

If Z is a standard normal random variable, find the value of z that has the following probabilities:
a. P(Z ≤ z) = 0.3228.
b. P(Z ≥ z) = 0.8289.

Accepted Answer

The answer of If Z is a standard normal random...

Question 7

A bank has determined that the monthly balances of the saving accounts of its customers are normally distributed, with an average balance of $1200 and a standard deviation of $250. What proportions of the customers have monthly balances:
a. less than $1000?
b. more than $1125?
c. between $950 and $1075?

Accepted Answer

a. 0.2119.

Question 8

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?

Accepted Answer

a. f(x) = 1/4, 1@#LAT-DLM& x @#LAT-DLM&

Question 9

Let z1 be a z-score that is unknown but identifiable by position and area. If the area to the right of z1 is 0.7291, the value of z1 is -0.61.

Accepted Answer

A) True 
 B)False

Question 10

The time it takes a student to complete a 3-hour business statistics sample exam paper is uniformly distributed between 150 and 230 minutes.
a. What is the probability density function for this uniform distribution?
b. Find the probability that a student will take no more than 180 minutes to complete the sample exam paper.
c. Find the probability that a student will take no less than 205 minutes to complete the sample exam paper.
d. What is the expected amount of time it takes a student to complete the sample exam paper?
e. What is the standard deviation for the amount of time it takes a student to complete the sample exam paper?

Accepted Answer

a. f(x) = 1/80, 150

Question 11

If Z is a standard normal random variable, find the following probabilities.
a. P(Z $\leq$ 2.33).
b. P(Z $\geq$ 1.65).
c. P(-0.58 $\leq$ Z $\leq$ 1.58).
d. P(Z $\leq$ -2.27).

Accepted Answer

a. 0.9901.

Question 12

If the random variable X is exponentially distributed with parameter $\lambda$ = 1.75, then P(1.5 $\le$ X$\le$ 3.8), up to 4 decimal places, is: $\begin{array}{|l|l|}
\hline\text { A. } & 0.0711 . \
\hline \text { B. } & 0.0473 . \
\hline \text { C. } & 0.1184 . \
\hline \text { D. } & 0.4739 \
\hline
\end{array}$

Accepted Answer

The answer of If the random variable X is exponentially...

Question 13

Which of the following is always true for all probability density functions of continuous random variables? $\begin{array}{|l|l|}
\hline  A&\text {They are symmetrical. }\
\hline  B&\text { They are bell-shaped.}\
\hline  C&\text {The area under the curve is 1.0 . }\
\hline  D&\text {They have the same height. }\
\hline 
\end{array}$

Accepted Answer

The answer of Which of the following is always true...

Question 14

The normal approximation to the binomial distribution works best when the number of trials is large, and when the binomial distribution is symmetrical (like the normal).

Accepted Answer

A) True 
 B)False

Question 15

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.1949? $\begin{array}{|l|l|}
\hline \text { A. } & 0.51 . \
\hline \text { B. } & -0.51 . \
\hline \text { C. } & 0.86 . \
\hline \text { D. } & -0.86 . \
\hline
\end{array}$

Accepted Answer

The answer of Given that Z is a standard normal...

Question 16

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

Accepted Answer

A) True 
 B)False

Question 17

A fair coin is tossed 500 times. Approximate the probability that the number of tails observed is between 240 and 270 (inclusive).

Accepted Answer

The answer of A fair coin is tossed 500 times....

Question 18

The mean of the exponential distribution equals the mean of the Poisson distribution only when the former distribution has a mean equal to: $\begin{array}{|l|l|}
\hline\text { A. } & 1.0 . \
\hline \text { B. } & 0.50 \
\hline \text { C. } & 0.25 . \
\hline \text { D. } & \text { any value smaller than } 1.0 \
\hline
\end{array}$

Accepted Answer

The answer of The mean of the exponential distribution equals...

Question 19

A random variable X is standardised when each value of X has the mean of X subtracted from it, and the difference is divided by the standard deviation of X.

Accepted Answer

A) True 
 B)False

Question 20

Let X be a binomial random variable with n = 100 and p = 0.7. Approximate the following probabilities, using the normal distribution.
a. P(X = 75).
b. P(X $\le$  70).
c. P(X $\ge$  60).

Accepted Answer

a. 0.0484.

Exam 8: Continuous Probability Distributions

Using the standard normal curve, the area between z = 0 and z = 3.50 is about 0.50.

If the random variable X is exponentially distributed with λ\lambdaλ = 2 parameter, then the variance of the distribution is 0.5.

If X is a normal random variable with a mean of 78 and a standard deviation of 5, find the following probabilities: a. P(X ≤\le≤ 87). b. P(X ≥\ge≥ 91). c. P( ≤\le≤ X ≤\le≤ ).

If Z is a standard normal random variable, find the value z for which: a. P(0 ≤\leq≤ Z ≤\leq≤ z) = 0.276. b. P(Z ≥\geq≥ z) = 0.341. c. P(Z ≥\geq≥ z) = 0.819. d. P(-z ≤\leq≤ Z ≤\leq≤ z) = 0.785. e. P(Z ≤\leq≤ z) = 0.9279.

Which of the following is a characteristic of a normal distribution? A It is a symmetrical distribution. B The mean is always zero. C The mean, median and mode are all equal. D All of these choices are correct.

If Z is a standard normal random variable, find the value of z that has the following probabilities: a. P(Z ≤ z) = 0.3228. b. P(Z ≥ z) = 0.8289.

Let z1 be a z-score that is unknown but identifiable by position and area. If the area to the right of z1 is 0.7291, the value of z1 is -0.61.

If Z is a standard normal random variable, find the following probabilities. a. P(Z ≤\leq≤ 2.33). b. P(Z ≥\geq≥ 1.65). c. P(-0.58 ≤\leq≤ Z ≤\leq≤ 1.58). d. P(Z ≤\leq≤ -2.27).

If the random variable X is exponentially distributed with parameter λ\lambdaλ = 1.75, then P(1.5 ≤\le≤ X ≤\le≤ 3.8), up to 4 decimal places, is: A. 0.0711. B. 0.0473. C. 0.1184. D. 0.4739

Which of the following is always true for all probability density functions of continuous random variables? A They are symmetrical. B They are bell-shaped. C The area under the curve is 1.0 . D They have the same height.

The normal approximation to the binomial distribution works best when the number of trials is large, and when the binomial distribution is symmetrical (like the normal).

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.1949? A. 0.51. B. -0.51. C. 0.86. D. -0.86.

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

A fair coin is tossed 500 times. Approximate the probability that the number of tails observed is between 240 and 270 (inclusive).

The mean of the exponential distribution equals the mean of the Poisson distribution only when the former distribution has a mean equal to: A. 1.0. B. 0.50 C. 0.25. D. any value smaller than 1.0

A random variable X is standardised when each value of X has the mean of X subtracted from it, and the difference is divided by the standard deviation of X.

Let X be a binomial random variable with n = 100 and p = 0.7. Approximate the following probabilities, using the normal distribution. a. P(X = 75). b. P(X ≤\le≤ 70). c. P(X ≥\ge≥ 60).

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

If the random variable X is exponentially distributed with $\lambda$ = 2 parameter, then the variance of the distribution is 0.5.

If X is a normal random variable with a mean of 78 and a standard deviation of 5, find the following probabilities: a. P(X $\le$ 87). b. P(X $\ge$ 91). c. P( $\le$ X $\le$ ).

If Z is a standard normal random variable, find the value z for which: a. P(0 $\leq$ Z $\leq$ z) = 0.276. b. P(Z $\geq$ z) = 0.341. c. P(Z $\geq$ z) = 0.819. d. P(-z $\leq$ Z $\leq$ z) = 0.785. e. P(Z $\leq$ z) = 0.9279.

Let z₁ be a z-score that is unknown but identifiable by position and area. If the area to the right of z₁ is 0.7291, the value of z₁ is -0.61.

If Z is a standard normal random variable, find the following probabilities. a. P(Z $\leq$ 2.33). b. P(Z $\geq$ 1.65). c. P(-0.58 $\leq$ Z $\leq$ 1.58). d. P(Z $\leq$ -2.27).

If the random variable X is exponentially distributed with parameter $\lambda$ = 1.75, then P(1.5 $\le$ X $\le$ 3.8), up to 4 decimal places, is: A. 0.0711. B. 0.0473. C. 0.1184. D. 0.4739

Let X be a binomial random variable with n = 100 and p = 0.7. Approximate the following probabilities, using the normal distribution. a. P(X = 75). b. P(X $\le$ 70). c. P(X $\ge$ 60).