Question 1

Given that the random variable X is normally distributed with a mean of 20 and a standard deviation of 7, P(28 F1F1F1S1F1F1F10 X F1F1F1S1F1F1F10 30) is:

Accepted Answer

A) 2 
B) 0.0507. 
C) 0.8729 
D) 0.9236 
A) 2 
B) 0.0507. 
C) 0.8729 
D) 0.9236

Question 2

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

Accepted Answer

A) True 
 B)False

Question 3

Given that Z is a standard normal variable, the value z for which P(Z F1F1F1S1F1F1F10 z) = 0.2580 is:

Accepted Answer

A) 0.70. 
B) 0.758. 
C) -0.65. 
D) 0.242. 
A) 0.70. 
B) 0.758. 
C) -0.65. 
D) 0.242.

Question 4

In the normal distribution, the curve is asymptotic but never intercepts the horizontal axis either to the left or right.

Accepted Answer

A) True 
 B)False

Question 5

If the random variable X is exponentially distributed with parameter $\lambda$ = 4, then the probability P(X $\leq$ 0.25), up to 4 decimal places, is:

Accepted Answer

A) 0.6321. 
B) 0.3679. 
C) 0.2500. 
D) None of these choices are correct. 
A) 0.6321. 
B) 0.3679. 
C) 0.2500. 
D) None of these choices are correct.

Question 6

If X is a normal random variable with a mean of 45 and a standard deviation of 8, find the following probabilities: 
a. $P ( X \geq 50 )$
b. $P ( X \leq 32 )$
c. $P ( 37 \leq X \leq 48 )$
d. $P ( 50 \leq X \leq 60 )$
e. $P ( X = 45 )$

Accepted Answer

a. 0.2643.
b. 0.0516

Question 7

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 8

Let X be a normally distributed random variable with a mean of 12 and a standard deviation of 1.5. What proportions of the values of X are:
a. less than 14?
b. more than 8?
c. between 10 and 13?

Accepted Answer

a. 0.9082.

Question 9

Given that Z is a standard normal random variable, a positive z value means that:

Accepted Answer

A) the value z is to the left of the mean. 
B) the value z is to the right of the median. 
C) the z value is to the right of the mean. 
D) both B and C are correct. 
A) the value z is to the left of the mean. 
B) the value z is to the right of the median. 
C) the z value is to the right of the mean. 
D) both B and C are correct.

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

The answer of The time it takes a student to...

Question 11

In the standard normal distribution, z0.05 = 1.645 means that there is a 5% chance that the standard normal random variable Z assumes a value above 1.645.

Accepted Answer

A) True 
 B)False

Question 12

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

Accepted Answer

A) is always greater than 2.0. 
B) is always greater than 1.0. 
C) is always equal to 1.0. 
D) cannot assume a specific value. 
A) is always greater than 2.0. 
B) is always greater than 1.0. 
C) is always equal to 1.0. 
D) cannot assume a specific value.

Question 13

If we standardise the normal curve, we express the original x values in terms of their number of standard deviations away from the mean.

Accepted Answer

A) True 
 B)False

Question 14

A continuous random variable X has the probability density function f(x) = 2e-2x, x F1F1F1S1F1F1F10 0.
a. Find the mean and standard deviation of X.
b. What is the probability that X is between 1 and 3?
c. What is the probability that X is at most 2?

Accepted Answer

a. X is an exponential random

Question 15

In the exponential distribution, the value of x can be any of an infinite number of values in the given range.

Accepted Answer

A) True 
 B)False

Question 16

Find the following probabilities.
a. P(X $\leq$ 7).
b. P(X $\geq$ 8).
c. P(X = 9). $$\text { Hint: } P ( a \leq x \leq b ) = \int _ { a } ^ { b } f ( x ) d x$$

Accepted Answer

a. 0.91.
b

Question 17

The weights of cans of soup produced by a company are normally distributed, with a mean of 150 g and a standard deviation of 5 g.
a. What is the probability that a can of soup selected randomly from the entire production will weigh less than 143 g?
b. Determine the minimum weight of the heaviest 5% of all cans of soup produced.
c. If 28 390 of the cans of soup of the entire production weigh at least 157.5 g, how many cans of soup have been produced?

Accepted Answer

a. 0.0808

Question 18

Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 7 kg and a standard deviation of 2.5 kg.
a. What proportion of the dieters lost more than 10 kg?
b. What proportion of the dieters gained weight?
c. If a dieter is selected at random, what is the probability that the dieter lost at most 5 kg?

Accepted Answer

a. 0.1151.

Question 19

A standard normal distribution is a normal distribution with:

Accepted Answer

A) a mean of zero and a standard deviation of one. 
B) a mean of one and a standard deviation of zero. 
C) a mean usually larger than the standard deviation. 
D) a mean always larger than the standard deviation. 
A) a mean of zero and a standard deviation of one. 
B) a mean of one and a standard deviation of zero. 
C) a mean usually larger than the standard deviation. 
D) a mean always larger than the standard deviation.

Question 20

Given that Z is a standard normal random variable, P(-1.23 F1F1F1S1F1F1F10 Z F1F1F1S1F1F1F101.89) is:

Accepted Answer

A) 0.1903. 
B) 0.9706. 
C) 0.8907. 
D) 0.8613. 
A) 0.1903. 
B) 0.9706. 
C) 0.8907. 
D) 0.8613.

Given that the random variable X is normally distributed with a mean of 20 and a standard deviation of 7, P(28  X  30) is:

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 variable, the value z for which P(Z  z) = 0.2580 is:

In the normal distribution, the curve is asymptotic but never intercepts the horizontal axis either to the left or right.

If the random variable X is exponentially distributed with parameter $\lambda$ = 4, then the probability P(X $\leq$ 0.25), up to 4 decimal places, is:

If X is a normal random variable with a mean of 45 and a standard deviation of 8, find the following probabilities: a. $P ( X \geq 50 )$ b. $P ( X \leq 32 )$ c. $P ( 37 \leq X \leq 48 )$ d. $P ( 50 \leq X \leq 60 )$ e. $P ( X = 45 )$

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).

Let X be a normally distributed random variable with a mean of 12 and a standard deviation of 1.5. What proportions of the values of X are: a. less than 14? b. more than 8? c. between 10 and 13?

Given that Z is a standard normal random variable, a positive z value means that:

In the standard normal distribution, z0.05 = 1.645 means that there is a 5% chance that the standard normal random variable Z assumes a value above 1.645.

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

If we standardise the normal curve, we express the original x values in terms of their number of standard deviations away from the mean.

A continuous random variable X has the probability density function f(x) = 2e-2x, x  0. a. Find the mean and standard deviation of X. b. What is the probability that X is between 1 and 3? c. What is the probability that X is at most 2?

In the exponential distribution, the value of x can be any of an infinite number of values in the given range.

Find the following probabilities. a. P(X $\leq$ 7). b. P(X $\geq$ 8). c. P(X = 9). $\text { Hint: } P ( a \leq x \leq b ) = \int _ { a } ^ { b } f ( x ) d x$

A standard normal distribution is a normal distribution with:

Given that Z is a standard normal random variable, P(-1.23  Z 1.89) is:

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

Given that the random variable X is normally distributed with a mean of 20 and a standard deviation of 7, P(28  X  30) is:

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 variable, the value z for which P(Z  z) = 0.2580 is:

In the normal distribution, the curve is asymptotic but never intercepts the horizontal axis either to the left or right.

If the random variable X is exponentially distributed with parameter λ\lambdaλ = 4, then the probability P(X ≤\leq≤ 0.25), up to 4 decimal places, is:

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).

Let X be a normally distributed random variable with a mean of 12 and a standard deviation of 1.5. What proportions of the values of X are: a. less than 14? b. more than 8? c. between 10 and 13?

Given that Z is a standard normal random variable, a positive z value means that:

In the standard normal distribution, z0.05 = 1.645 means that there is a 5% chance that the standard normal random variable Z assumes a value above 1.645.

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

If we standardise the normal curve, we express the original x values in terms of their number of standard deviations away from the mean.

A continuous random variable X has the probability density function f(x) = 2e-2x, x  0. a. Find the mean and standard deviation of X. b. What is the probability that X is between 1 and 3? c. What is the probability that X is at most 2?

In the exponential distribution, the value of x can be any of an infinite number of values in the given range.

Find the following probabilities. a. P(X ≤\leq≤ 7). b. P(X ≥\geq≥ 8). c. P(X = 9). Hint: P(a≤x≤b)=∫abf(x)dx\text { Hint: } P ( a \leq x \leq b ) = \int _ { a } ^ { b } f ( x ) d x Hint: P(a≤x≤b)=∫ab​f(x)dx

A standard normal distribution is a normal distribution with:

Given that Z is a standard normal random variable, P(-1.23  Z 1.89) is:

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 the random variable X is exponentially distributed with parameter $\lambda$ = 4, then the probability P(X $\leq$ 0.25), up to 4 decimal places, is:

Find the following probabilities. a. P(X $\leq$ 7). b. P(X $\geq$ 8). c. P(X = 9). $\text { Hint: } P ( a \leq x \leq b ) = \int _ { a } ^ { b } f ( x ) d x$