Question 1

Excel's NORM.INV function can be used to compute

Accepted Answer

A) cumulative probabilities for a standard normal z value 
B) the standard normal z value given a cumulative probability 
C) cumulative probabilities for a normally distributed x value 
D) the normally distributed x value given a cumulative probability 
A) cumulative probabilities for a standard normal z value 
B) the standard normal z value given a cumulative probability 
C) cumulative probabilities for a normally distributed x value 
D) the normally distributed x value given a cumulative probability D

Question 2

X is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that x is between 1.48 and 15.56 is

Accepted Answer

A) 0.0222 
B) 0.4190 
C) 0.5222 
D) 0.9190 
A) 0.0222 
B) 0.4190 
C) 0.5222 
D) 0.9190 D

Question 3

Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6.
a.What is the probability that a randomly selected exam will have a score of at least 71?
b.What percentage of exams will have scores between 89 and 92?
c.If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award?
d.If there were 334 exams with scores of at least 89, how many students took the exam?

Accepted Answer

a..9332
b..04
c.91.76
d.5000

Question 4

Z is a standard normal variable. Find the value of z in the following.
a. The area between 0 and z is 0.4678.
b. The area to the right of z is 0.1112.
c. The area to the left of z is 0.8554
d. The area between -z and z is 0.754.
e. The area to the left of -z is 0.0681.
f. The area to the right of -z is 0.9803.

Accepted Answer

a.1.85
b.1

Question 5

A light bulb manufacturer claims its light bulbs will last 500 hours on the average. The lifetime of a light bulb is assumed to follow an exponential distribution.
a. What is the probability that the light bulb will have to be replaced within 500 hours?
b. What is the probability that the light bulb will last more than 1000 hours?
c. What is the probability that the light bulb will last between 200 and 800 hours.

Accepted Answer

a. .632
b.

Question 6

Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable is

Accepted Answer

A) uniformly distributed 
B) normally distributed 
C) exponentially distributed 
D) Poisson distributed 
A) uniformly distributed 
B) normally distributed 
C) exponentially distributed 
D) Poisson distributed

Question 7

Z is a standard normal random variable. The P(-1.96 $\le$ z $\le$ -1.4) equals

Accepted Answer

A) 0.8942 
B) 0.0558 
C) 0.475 
D) 0.4192 
A) 0.8942 
B) 0.0558 
C) 0.475 
D) 0.4192

Question 8

The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6.
a.Define the random variable in words.
b.What is the probability that a randomly selected bill will be at least $39.10?
c.What percentage of the bills will be less than $16.90?
d.What are the minimum and maximum of the middle 95% of the bills?
e.If twelve of one day's bills had a value of at least $43.06, how many bills did the restaurant collect on that day?

Accepted Answer

a.the daily dinner b

Question 9

X is a exponentially distributed random variable with a mean of 10. Use Excel to calculate the following:
a.P(x $\le$ 15)
b.P(8 $\le$ x $\le$ 12)
c.P(x $\ge$ 8)

Accepted Answer

a.P(x @#LAT-DLM& 15)
=EXPON.DIST(15,1/10

Question 10

The monthly income of residents of Daisy City is normally distributed with a mean of $3000 and a standard deviation of $500.
a.Define the random variable in words.
b.The mayor of Daisy City makes $2,250 a month. What percentage of Daisy City's residents has incomes that are more than the mayor's?
c.Individuals with incomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes?
d.What are the minimum and the maximum incomes of the middle 95% of the residents?
e.Two hundred residents have incomes of at least $4,440 per month. What is the population of Daisy City?

Accepted Answer

a.the monthly income

Question 11

An exponential probability distribution

Accepted Answer

A) is a continuous distribution 
B) is a discrete distribution 
C) can be either continuous or discrete 
D) must be normally distributed 
A) is a continuous distribution 
B) is a discrete distribution 
C) can be either continuous or discrete 
D) must be normally distributed

Question 12

Exhibit 6-5
The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.
-Refer to Exhibit 6-5. What is the probability that a randomly selected item weighs exactly 8 ounces?

Accepted Answer

A) 0.5 
B) 1.0 
C) 0.3413 
D) None of the alternative answers is correct. 
A) 0.5 
B) 1.0 
C) 0.3413 
D) None of the alternative answers is correct.

Question 13

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability of assembling the product between 7 to 9 minutes is

Accepted Answer

A) zero 
B) 0.50 
C) 0.20 
D) 1 
A) zero 
B) 0.50 
C) 0.20 
D) 1

Question 14

For a standard normal distribution, a negative value of z indicates

Accepted Answer

A) a mistake has been made in computations, because z is always positive 
B) the area corresponding to the z is negative 
C) the z is to the left of the mean 
D) the z is to the right of the mean 
A) a mistake has been made in computations, because z is always positive 
B) the area corresponding to the z is negative 
C) the z is to the left of the mean 
D) the z is to the right of the mean

Question 15

X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that x is greater than 10.52 is

Accepted Answer

A) 0.0029 
B) 0.0838 
C) 0.4971 
D) 0.9971 
A) 0.0029 
B) 0.0838 
C) 0.4971 
D) 0.9971

Question 16

The weekly earnings of fast-food restaurant employees are normally distributed with a mean of $395. If only 1.1% of the employees have a weekly income of more than $429.35, what is the value of the standard deviation of the weekly earnings of the employees?

Accepted Answer

Standard D

Question 17

The uniform probability distribution is used with

Accepted Answer

A) a continuous random variable 
B) a discrete random variable 
C) a normally distributed random variable 
D) any random variable 
A) a continuous random variable 
B) a discrete random variable 
C) a normally distributed random variable 
D) any random variable

Question 18

Exhibit 6-2
The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.
-Refer to Exhibit 6-2. The probability that she will finish her trip in 80 minutes or less is

Accepted Answer

A) 0.02 
B) 0.8 
C) 0.2 
D) 1.00 
A) 0.02 
B) 0.8 
C) 0.2 
D) 1.00

Question 19

The miles-per-gallon obtained by the 2013 model Q cars is normally distributed with a mean of 22 miles-per-gallon and a standard deviation of 5 miles-per-gallon.
a.What is the probability that a car will get between 13.35 and 35.1 miles-per-gallon?
b.What is the probability that a car will get more than 29.6 miles-per-gallon?
c.What is the probability that a car will get less than 21 miles-per-gallon?
d.What is the probability that a car will get exactly 22 miles-per-gallon?

Accepted Answer

a.0.9538
b

Question 20

A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation.

Accepted Answer

Mean = 113

Excel's NORM.INV function can be used to compute

X is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that x is between 1.48 and 15.56 is

Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable is

Z is a standard normal random variable. The P(-1.96 $\le$ z $\le$ -1.4) equals

X is a exponentially distributed random variable with a mean of 10. Use Excel to calculate the following: a.P(x $\le$ 15) b.P(8 $\le$ x $\le$ 12) c.P(x $\ge$ 8)

An exponential probability distribution

Exhibit 6-5 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. -Refer to Exhibit 6-5. What is the probability that a randomly selected item weighs exactly 8 ounces?

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability of assembling the product between 7 to 9 minutes is

For a standard normal distribution, a negative value of z indicates

X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that x is greater than 10.52 is

The weekly earnings of fast-food restaurant employees are normally distributed with a mean of $395. If only 1.1% of the employees have a weekly income of more than $429.35, what is the value of the standard deviation of the weekly earnings of the employees?

The uniform probability distribution is used with

Exhibit 6-2 The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. -Refer to Exhibit 6-2. The probability that she will finish her trip in 80 minutes or less is

A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation.

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Tests of Goodness of Fit, Independence and Multiple Proportions

Experimental Design and Analysis of Variance

Simple Linear Regression

Multiple Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Decision Analysis

Sample Survey

Filters

Exam 6: Continuous Probability Distributions

Excel's NORM.INV function can be used to compute

X is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that x is between 1.48 and 15.56 is

Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable is

Z is a standard normal random variable. The P(-1.96 ≤\le≤ z ≤\le≤ -1.4) equals

X is a exponentially distributed random variable with a mean of 10. Use Excel to calculate the following: a.P(x ≤\le≤ 15) b.P(8 ≤\le≤ x ≤\le≤ 12) c.P(x ≥\ge≥ 8)

An exponential probability distribution

Exhibit 6-5 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. -Refer to Exhibit 6-5. What is the probability that a randomly selected item weighs exactly 8 ounces?

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability of assembling the product between 7 to 9 minutes is

For a standard normal distribution, a negative value of z indicates

X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that x is greater than 10.52 is

The weekly earnings of fast-food restaurant employees are normally distributed with a mean of $395. If only 1.1% of the employees have a weekly income of more than $429.35, what is the value of the standard deviation of the weekly earnings of the employees?

The uniform probability distribution is used with

Exhibit 6-2 The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. -Refer to Exhibit 6-2. The probability that she will finish her trip in 80 minutes or less is

A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation.

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Tests of Goodness of Fit, Independence and Multiple Proportions

Experimental Design and Analysis of Variance

Simple Linear Regression

Multiple Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Decision Analysis

Sample Survey

Filters

Z is a standard normal random variable. The P(-1.96 $\le$ z $\le$ -1.4) equals

X is a exponentially distributed random variable with a mean of 10. Use Excel to calculate the following: a.P(x $\le$ 15) b.P(8 $\le$ x $\le$ 12) c.P(x $\ge$ 8)