Question 1

Find the value of σ if it is known that X is normally distributed with mean 5 and 14.92% of the values are above 8?

Accepted Answer

A) 2.14 
B) 2.88 
C) 3 
D) None of these choices are correct. 
A) 2.14 
B) 2.88 
C) 3 
D) None of these choices are correct.

Question 2

If Z is a standard normal random variable, then P(-2.28 F1F1F1S1F1F1F10 Z F1F1F1S1F1F1F10 -1.96 ) is:

Accepted Answer

A) 0.0250. 
B) 0.0146. 
C) −0.0146. 
D) 0.0137. 
A) 0.0250. 
B) 0.0146. 
C) −0.0146. 
D) 0.0137.

Question 3

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?

Accepted Answer

A) 11.63. 
B) 61.63. 
C) 63.16. 
D) 16.31. 
A) 11.63. 
B) 61.63. 
C) 63.16. 
D) 16.31.

Question 4

The publisher of a daily newspaper claims that 90% of its subscribers are under the age of 30. Suppose that a sample of 300 subscribers is selected at random. Assuming the claim is correct, calculate the probability of finding at least 260 subscribers in the sample under the age of 30.

Accepted Answer

The answer of The publisher of a daily newspaper claims...

Question 5

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

Accepted Answer

A) True 
 B)False

Question 6

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 7

Given that X is a binomial random variable, the binomial probability P(X $\geq$ x) is approximated by the area under a normal curve to the right of:

Accepted Answer

A) x - 0.5. 
B) x + 0.5. 
C) x - 1. 
D) x + 1. 
A) x - 0.5. 
B) x + 0.5. 
C) x - 1. 
D) x + 1.

Question 8

What proportion of the data from a normal distribution is within 2 standard deviations of the mean?

Accepted Answer

A) 0.3413. 
B) 0.4772. 
C) 0.6826. 
D) 0.9544. 
A) 0.3413. 
B) 0.4772. 
C) 0.6826. 
D) 0.9544.

Question 9

Given that Z is a standard normal variable, the value z for which P(Z $\leq$ z) = 0.6736 is:

Accepted Answer

A) 0.1736. 
B) 0.45. 
C) -0.1736. 
D) -0.45. 
A) 0.1736. 
B) 0.45. 
C) -0.1736. 
D) -0.45.

Question 10

Let X be an exponential random variable with F1F1F1S1F1F1F10 = 2.50. Find the following probabilities. 
a. $P ( X \geq 1.5 )$
b. $P ( X \leq 1 )$
c. $P ( 0.25 \leq X \leq 0.78 )$
d. $P ( X = 0.41 )$

Accepted Answer

a. 0.0235.

Question 11

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 12

The time it takes a technician to fix a computer problem is exponentially distributed, with a mean of 15 minutes.
a. What is the probability density function for the time it takes a technician to fix a computer problem?
b. What is the probability that it will take a technician less than 10 minutes to fix a computer problem?
c. What is the variance of the time it takes a technician to fix a computer problem?
d. What is the probability that it will take a technician between 10 to 15 minutes to fix a computer problem?

Accepted Answer

a. 11ec93b1_d54c_3ac

Question 13

A smaller standard deviation of a normal distribution indicates that the distribution becomes:

Accepted Answer

A) more skewed to the left. 
B) flatter and wider. 
C) narrower and more peaked. 
D) symmetrical. 
A) more skewed to the left. 
B) flatter and wider. 
C) narrower and more peaked. 
D) symmetrical.

Question 14

Like the normal distribution, the exponential density function f(x):

Accepted Answer

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

Question 15

The recent average starting salary for new college graduates in computer information systems is $47 500. Assume that salaries are normally distributed, with a standard deviation of $4500.
a. What is the probability of a new graduate receiving a salary between $45 000 and $50 000?
b. What is the probability of a new graduate getting a starting salary in excess of $55 000?
c. What percentage of starting salaries are no more than $42 250?
d. What is the cut-off for the bottom 5% of the salaries?
e. What is the cut-off for the top 3% of the salaries?

Accepted Answer

a. 0.4246.
b. 0.0475

Question 16

The exponential distribution is suitable to model the length of time that elapses before the first telephone call is received by a switchboard.

Accepted Answer

A) True 
 B)False

Question 17

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 18

The values of zA are the 100(1 - A)th percentiles of a standard normal random variable.

Accepted Answer

A) True 
 B)False

Question 19

The function f(x) that defines the probability distribution of a continuous random variable X is a:

Accepted Answer

A) binomial function. 
B) normal function. 
C) Poisson function. 
D) probability density function. 
A) binomial function. 
B) normal function. 
C) Poisson function. 
D) probability density function.

Question 20

Which of the following distributions is considered the cornerstone distribution of statistical inference?

Accepted Answer

A) Binomial distribution. 
B) Normal distribution. 
C) Poisson distribution. 
D) Uniform distribution. 
A) Binomial distribution. 
B) Normal distribution. 
C) Poisson distribution. 
D) Uniform distribution.

Find the value of σ if it is known that X is normally distributed with mean 5 and 14.92% of the values are above 8?

If Z is a standard normal random variable, then P(-2.28  Z  -1.96 ) is:

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?

The publisher of a daily newspaper claims that 90% of its subscribers are under the age of 30. Suppose that a sample of 300 subscribers is selected at random. Assuming the claim is correct, calculate the probability of finding at least 260 subscribers in the sample under the age of 30.

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 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.

Given that X is a binomial random variable, the binomial probability P(X $\geq$ x) is approximated by the area under a normal curve to the right of:

What proportion of the data from a normal distribution is within 2 standard deviations of the mean?

Given that Z is a standard normal variable, the value z for which P(Z $\leq$ z) = 0.6736 is:

Let X be an exponential random variable with  = 2.50. Find the following probabilities. a. $P ( X \geq 1.5 )$ b. $P ( X \leq 1 )$ c. $P ( 0.25 \leq X \leq 0.78 )$ d. $P ( X = 0.41 )$

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.

A smaller standard deviation of a normal distribution indicates that the distribution becomes:

Like the normal distribution, the exponential density function f(x):

The exponential distribution is suitable to model the length of time that elapses before the first telephone call is received by a switchboard.

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. $P ( Z \leq - 2.27 )$

The values of zA are the 100(1 - A)th percentiles of a standard normal random variable.

The function f(x) that defines the probability distribution of a continuous random variable X is a:

Which of the following distributions is considered the cornerstone distribution of statistical inference?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

Exam 8: Continuous Probability Distributions

Find the value of σ if it is known that X is normally distributed with mean 5 and 14.92% of the values are above 8?

If Z is a standard normal random variable, then P(-2.28  Z  -1.96 ) is:

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?

The publisher of a daily newspaper claims that 90% of its subscribers are under the age of 30. Suppose that a sample of 300 subscribers is selected at random. Assuming the claim is correct, calculate the probability of finding at least 260 subscribers in the sample under the age of 30.

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 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.

Given that X is a binomial random variable, the binomial probability P(X ≥\geq≥ x) is approximated by the area under a normal curve to the right of:

What proportion of the data from a normal distribution is within 2 standard deviations of the mean?

Given that Z is a standard normal variable, the value z for which P(Z ≤\leq≤ z) = 0.6736 is:

Let X be an exponential random variable with  = 2.50. Find the following probabilities. a. P(X≥1.5)P ( X \geq 1.5 )P(X≥1.5) b. P(X≤1)P ( X \leq 1 )P(X≤1) c. P(0.25≤X≤0.78)P ( 0.25 \leq X \leq 0.78 )P(0.25≤X≤0.78) d. P(X=0.41)P ( X = 0.41 )P(X=0.41)

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.

A smaller standard deviation of a normal distribution indicates that the distribution becomes:

Like the normal distribution, the exponential density function f(x):

The exponential distribution is suitable to model the length of time that elapses before the first telephone call is received by a switchboard.

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

The values of zA are the 100(1 - A)th percentiles of a standard normal random variable.

The function f(x) that defines the probability distribution of a continuous random variable X is a:

Which of the following distributions is considered the cornerstone distribution of statistical inference?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

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.

Given that X is a binomial random variable, the binomial probability P(X $\geq$ x) is approximated by the area under a normal curve to the right of:

Given that Z is a standard normal variable, the value z for which P(Z $\leq$ z) = 0.6736 is:

Let X be an exponential random variable with  = 2.50. Find the following probabilities. a. $P ( X \geq 1.5 )$ b. $P ( X \leq 1 )$ c. $P ( 0.25 \leq X \leq 0.78 )$ d. $P ( X = 0.41 )$

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. $P ( Z \leq - 2.27 )$