Question 1

Find the value of µ, if X is a normal random variable, with standard deviation 2, and 2.5% of the values are below 1?

Accepted Answer

A)   - 2.92 
B)   1.96 
C)   4.92 
D) None of these choices are correct. 
A)   - 2.92 
B)   1.96 
C)   4.92 
D) None of these choices are correct.

Question 2

Let X be a binomial random variable with n = 25 and p = 0.6. Approximate the following probabilities, using the normal distribution.
a. P(X $\geq$ 20).
b. P(X $\leq$ 15).
c. P(X = 10).

Accepted Answer

a. 0.0329.

Question 3

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 4

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?

Accepted Answer

A)  0.92 . 
B)   - 0.05 . 
C)   0.05 
D)   - 0.92 . 
A)  0.92 . 
B)   - 0.05 . 
C)   0.05 
D)   - 0.92 .

Question 5

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

Accepted Answer

A) True 
 B)False

Question 6

For a normal curve, if the mean is 20 minutes and the standard deviation is 5 minutes, the area to the right of 13 minutes is 0.9192.

Accepted Answer

A) True 
 B)False

Question 7

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 8

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 9

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?

Accepted Answer

A)  Exponential. 
B)  Normal. 
C)  Poisson. 
D)  Uniform. 
A)  Exponential. 
B)  Normal. 
C)  Poisson. 
D)  Uniform.

Question 10

The mean of any normal distribution is always zero.

Accepted Answer

A) True 
 B)False

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

The scores of high-school students sitting a mathematics exam were normally distributed, with a mean of 86 and a standard deviation of 4.
a. What is the probability that a randomly selected student will have a score of 80 or less?
b. If there were 97 680 students with scores higher than 91, how many students took the test?

Accepted Answer

a. 0.0668

Question 13

If X is a normal random variable with a standard deviation of 10, then 3X has a standard deviation equal to:

Accepted Answer

A)   10 . 
B)  13 . 
C)   30 . 
D)  90 . 
A)   10 . 
B)  13 . 
C)   30 . 
D)  90 .

Question 14

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

Accepted Answer

A)  0.0250 . 
B)  0.0146 . 
C)  - 0.0104 . 
D)  0.0 .0104 . 
A)  0.0250 . 
B)  0.0146 . 
C)  - 0.0104 . 
D)  0.0 .0104 .

Question 15

A certain brand of flood lamps has a lifetime that is normally distributed with a mean of 3750 hours and a standard deviation of 300 hours.
a. What proportion of these lamps will last for more than 4000 hours?
b. What lifetime should the manufacturer advertise for these lamps in order that only 2% of the lamps will burn out before the advertised lifetime?

Accepted Answer

The answer of A certain brand of flood lamps has...

Question 16

If the random variable X is exponentially distributed with parameter $$\lambda$$ = 3, then P(X $$\geq$$ 2), up to 4 decimal places, is:

Accepted Answer

A)  0.3333 . 
B)   0.5000 . 
C)  0.6667 
D)  0.0025 . 
A)  0.3333 . 
B)   0.5000 . 
C)  0.6667 
D)  0.0025 .

Question 17

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 18

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 19

If the random variable X is normally distributed with a mean of 75 and a standard deviation of 8, then P(X ≤ 75) is:

Accepted Answer

A)   0.125 . 
B)   0.975 . 
C)  0.625 . 
D)   0.500 . 
A)   0.125 . 
B)   0.975 . 
C)  0.625 . 
D)   0.500 .

Question 20

If Z is a standard normal random variable, find the value z for which:
a. P(0 $\leq$ Z $\leq$ z) = 0.35.
b. P(-z $\leq$ Z $\leq$ z) = 0.142.
c. P(-z $\leq$ Z $\leq$ 0) = 0.441.

Accepted Answer

a. 1.04.
b

Exam 8: Continuous Probability Distributions

Find the value of µ, if X is a normal random variable, with standard deviation 2, and 2.5% of the values are below 1?

Let X be a binomial random variable with n = 25 and p = 0.6. Approximate the following probabilities, using the normal distribution. a. P(X ≥\geq≥ 20). b. P(X ≤\leq≤ 15). c. P(X = 10).

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

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?

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

For a normal curve, if the mean is 20 minutes and the standard deviation is 5 minutes, the area to the right of 13 minutes is 0.9192.

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

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

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?

The mean of any normal distribution is always zero.

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 X is a normal random variable with a standard deviation of 10, then 3X has a standard deviation equal to:

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

If the random variable X is exponentially distributed with parameter λ\lambdaλ = 3, then P(X ≥\geq≥ 2), up to 4 decimal places, is:

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.

If the random variable X is normally distributed with a mean of 75 and a standard deviation of 8, then P(X ≤ 75) is:

If Z is a standard normal random variable, find the value z for which: a. P(0 ≤\leq≤ Z ≤\leq≤ z) = 0.35. b. P(-z ≤\leq≤ Z ≤\leq≤ z) = 0.142. c. P(-z ≤\leq≤ Z ≤\leq≤ 0) = 0.441.

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

Let X be a binomial random variable with n = 25 and p = 0.6. Approximate the following probabilities, using the normal distribution. a. P(X $\geq$ 20). b. P(X $\leq$ 15). c. P(X = 10).

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 Z is a standard normal random variable, then P(-2.28 $\le$ Z $\le$ -1.96 ) is:

If the random variable X is exponentially distributed with parameter $\lambda$ = 3, then P(X $\geq$ 2), up to 4 decimal places, is:

If Z is a standard normal random variable, find the value z for which: a. P(0 $\leq$ Z $\leq$ z) = 0.35. b. P(-z $\leq$ Z $\leq$ z) = 0.142. c. P(-z $\leq$ Z $\leq$ 0) = 0.441.