Question 1

For a standard normal distribution, the probability of z F1F1F1S1F1F1F10 0 is

Accepted Answer

A) zero 
B) -0.5 
C) 0.5 
D) one 
A) zero 
B) -0.5 
C) 0.5 
D) one

Question 2

The township of Middleton sets the speed limit on its roads by conducting a traffic study and determining the speed (to the nearest 5 miles per hour) at which 80% of the drivers travel at or below. A study was done on Brown's Dock Road that indicated driver's speeds follow a normal distribution with a mean of 36.25 miles per hour and a variance of 6.25.
a. What should the speed limit be?
b. What percent of the drivers travel below that speed?

Accepted Answer

a. 40 mile

Question 3

The length of time it takes students to complete a statistics examination is uniformly distributed and varies between 40 and 60 minutes.
a.Find the mathematical expression for the probability density function.
b.Compute the probability that a student will take between 45 and 50 minutes to complete the examination.
c.Compute the probability that a student will take no more than 40 minutes to complete the examination.
d.What is the expected amount of time it takes a student to complete the examination?
e.What is the variance for the amount of time it takes a student to complete the examination?

Accepted Answer

a.f(x) F1F1F1S1F1F1F10 0.05 f

Question 4

Exhibit 6-6
The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles.
-Refer to Exhibit 6-6. What is the probability that a randomly selected tire will have a life of exactly 47,500 miles?

Accepted Answer

A) 0.4332 
B) 0.9332 
C) 0.0668 
D) zero 
A) 0.4332 
B) 0.9332 
C) 0.0668 
D) zero

Question 5

The weights of the contents of cans of tomato paste produced by a company are normally distributed with a mean of 6 ounces and a standard deviation of 0.3 ounces.
a.What percentage of all cans produced contains more than 6.51 ounces of tomato paste?
b.What percentage of all cans produced contains less than 5.415 ounces?
c.What percentage of cans contains between 5.46 and 6.495 ounces?
d.Ninety-five percent of cans will contain at least how many ounces?
e.What percentage of cans contains between 6.3 and 6.6 ounces?

Accepted Answer

a.4.46%
b.

Question 6

The contents of soft drink bottles are normally distributed with a mean of twelve ounces and a standard deviation of one ounce.
a.What is the probability that a randomly selected bottle will contain more than ten ounces of soft drink?
b.What is the probability that a randomly selected bottle will contain between 9.5 and 11 ounces?
c.What percentage of the bottles will contain less than 10.5 ounces of soft drink?

Accepted Answer

a.0.9772
b

Question 7

Exhibit 6-6
The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles.
-Refer to Exhibit 6-6. What is the probability that a randomly selected tire will have a life of at least 30,000 miles?

Accepted Answer

A) 0.4772 
B) 0.9772 
C) 0.0228 
D) None of the alternative answers is correct. 
A) 0.4772 
B) 0.9772 
C) 0.0228 
D) None of the alternative answers is correct.

Question 8

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 9

In a standard normal distribution, the range of values of z is from

Accepted Answer

A) minus infinity to infinity 
B) -1 to 1 
C) 0 to 1 
D) -3.09 to 3.09 
A) minus infinity to infinity 
B) -1 to 1 
C) 0 to 1 
D) -3.09 to 3.09

Question 10

Given that z is a standard normal random variable, what is the value of z if the area to the left of z is 0.9382?

Accepted Answer

A) 1.8 
B) 1.54 
C) 2.1 
D) 1.77 
A) 1.8 
B) 1.54 
C) 2.1 
D) 1.77

Question 11

A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n)

Accepted Answer

A) normal probability distribution 
B) uniform probability distribution 
C) exponential probability distribution 
D) Poisson probability distribution 
A) normal probability distribution 
B) uniform probability distribution 
C) exponential probability distribution 
D) Poisson probability distribution

Question 12

X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that x is less than 9.7 is

Accepted Answer

A) 0.000 
B) 0.4931 
C) 0.0069 
D) 0.9931 
A) 0.000 
B) 0.4931 
C) 0.0069 
D) 0.9931

Question 13

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 14

The time it takes to hand carve a guitar neck is uniformly distributed between 110 and 190 minutes.
a.What is the probability that a guitar neck can be carved between 95 and 165 minutes?
b.What is the probability that the guitar neck can be carved between 120 and 200 minutes?
c.Determine the expected completion time for carving the guitar neck.
d.Compute the standard deviation.

Accepted Answer

a..6875
b.

Question 15

Exhibit 6-4
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.
-Refer to Exhibit 6-4. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?

Accepted Answer

A) 0.4772 
B) 0.9772 
C) 0.0228 
D) 0.5000 
A) 0.4772 
B) 0.9772 
C) 0.0228 
D) 0.5000

Question 16

The standard deviation of a standard normal distribution

Accepted Answer

A) is always equal to zero 
B) is always equal to one 
C) can be any positive value 
D) can be any value 
A) is always equal to zero 
B) is always equal to one 
C) can be any positive value 
D) can be any value

Question 17

The random variable x is known to be uniformly distributed between 70 and 90. The probability of x having a value between 80 to 95 is

Accepted Answer

A) 0.75 
B) 0.5 
C) 0.05 
D) 1 
A) 0.75 
B) 0.5 
C) 0.05 
D) 1

Question 18

The 9-month salaries at a daycare center are normally distributed with a mean of $19,000 and a standard deviation of $4,000.
a.What is the probability that an employee will have a salary between $12,520 and $13,480?
b.What is the probability that an employee will have a salary more than $11,880?
c.What is the probability that an employee will have a salary less than $28,440?

Accepted Answer

a.0.0312
b

Question 19

Delicious Candy markets a two-pound box of assorted chocolates. Because of imperfections in the candy making equipment, the actual weight of the chocolate has a uniform distribution ranging from 31.8 to 32.6 ounces.
a. Define a probability density function for the weight of the box of chocolate.
b. What is the probability that a box weighs (1) exactly 32 ounces; (2) more than 32.3 ounces; (3) less than 31.8 ounces?
c. The government requires that at least 60% of all products sold weigh at least as much as the stated weight. Is Delicious violating government regulations?

Accepted Answer

a. f(x) = 1.25 for 31.8 < x <

Question 20

A major department store has determined that its customers charge an average of $500 per month, with a standard deviation of $80. Assume the amounts of charges are normally distributed.
a.What percentage of customers charges more than $380 per month?
b.What percentage of customers charges less than $340 per month?
c.What percentage of customers charges between $644 and $700 per month?

Accepted Answer

a.93.32%
b

For a standard normal distribution, the probability of z  0 is

Exhibit 6-6 The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. -Refer to Exhibit 6-6. What is the probability that a randomly selected tire will have a life of exactly 47,500 miles?

Exhibit 6-6 The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. -Refer to Exhibit 6-6. What is the probability that a randomly selected tire will have a life of at least 30,000 miles?

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

In a standard normal distribution, the range of values of z is from

Given that z is a standard normal random variable, what is the value of z if the area to the left of z is 0.9382?

A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n)

X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that x is less than 9.7 is

An exponential probability distribution

The standard deviation of a standard normal distribution

The random variable x is known to be uniformly distributed between 70 and 90. The probability of x having a value between 80 to 95 is

Data and Statistics

Descriptive Statistics: Tabular and Graphical Presentations

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Comparisons Involving Means, Experimental Design, and Analysis of Variance

Comparisons Involving Proportions and a Test of Independence

Simple Linear Regression

Multiple Regression

Statistical Methods for Quality Control

Time Series Analysis and Forecastng

Filters

Exam 6: Continuous Probability Distributions

For a standard normal distribution, the probability of z  0 is

Exhibit 6-6 The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. -Refer to Exhibit 6-6. What is the probability that a randomly selected tire will have a life of exactly 47,500 miles?

Exhibit 6-6 The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. -Refer to Exhibit 6-6. What is the probability that a randomly selected tire will have a life of at least 30,000 miles?

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

In a standard normal distribution, the range of values of z is from

Given that z is a standard normal random variable, what is the value of z if the area to the left of z is 0.9382?

A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n)

X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that x is less than 9.7 is

An exponential probability distribution

The standard deviation of a standard normal distribution

The random variable x is known to be uniformly distributed between 70 and 90. The probability of x having a value between 80 to 95 is

Data and Statistics

Descriptive Statistics: Tabular and Graphical Presentations

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Comparisons Involving Means, Experimental Design, and Analysis of Variance

Comparisons Involving Proportions and a Test of Independence

Simple Linear Regression

Multiple Regression

Statistical Methods for Quality Control

Time Series Analysis and Forecastng

Filters