Bus Stats Midterm

Which of the following is a measure of dispersion?

interquartile range

Quantitative data refers to data obtained with a(n)

either interval or ratio scale

Exhibit 2-1 The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours

Frequency

0 - 9

20

10 - 19

80

20 - 29

200

30 - 39

100

Refer to Exhibit 2-1. The midpoint of the last class is

34.5

In a random sample of 200 items, 5 items were defective. An estimate of the percentage of defective items in the population is

2.5%

Exhibit 3-2

A researcher has collected the following sample data

5, 12, 6, 8, 5, 6, 7, 5, 12, 4

Refer to Exhibit 3-2. The mode is

5

In a data set, the number of elements will always be the same as the number of

Observations

Refer to Exhibit 1-3. Years of Experience is an example of ________ data.

Ratio

Exhibit 1-4 In many universities, students evaluate their professors by means of answering a questionnaire. Assume a questionnaire is distributed to a class of 45 students. Students are asked to answer the following: 1. Sex 2. Race (Black, White, Other) 3. Age 4. Number of hours completed 5. Grade point average 6. My instructor is a very effective teacher

1

2

3

4

5

strongly agree

moderately agree

neutral

moderately disagree

strongly disagree

Refer to Exhibit 1-4. How many variables are in this data set?

6

The number of cases will always be the same as the number of

elements

The relative frequency of a class is computed by

dividing the frequency of the class by n/sample size

If the mean of a normal distribution is negative,

None of these alternatives is correct.

The z score for the standard normal distribution

can be either negative or positive

Z is a standard normal random variable. The P (1.20 Z 1.85) equals

0.0829

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. Refer to Exhibit 6-1. The probability density function has what value in the interval between 6 and 10?

0.25

A measure of the average value of a random variable is called a(n)

expected value

In a standard normal distribution, the probability that Z is greater than zero is

0.5

Exhibit 6-6 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 6-6. What percentage of MBA's will have starting salaries of $34,000 to $46,000?

76.98%

The standard deviation is the

positive square root of the variance

Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.5?

0.0000

Exhibit 6-8 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 6-8. What is the probability that a randomly selected tire will have a life of exactly 47,500 miles?

0.0000

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is

the same for each interval

Exhibit 6-9 The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of $220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed. Refer to Exhibit 6-9. What is the probability that a randomly selected computer will have a price of at least $1,530?

0.0668

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

Poisson probability distribution

Exhibit 6-7 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 6-7. What percentage of items will weigh at least 11.7 ounces?

3.22%

Which of the following is not a characteristic of the normal probability distribution?

99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean

The total number of data items with a value less than the upper limit for the class is given by the

cumulative frequency distribution

The symbol s2 is used to represent

the variance of the population

The process of capturing, storing, and maintaining data is known as

data warehousing

Income is an example of a variable that uses the

ratio scale

The difference between the lower class limits of adjacent classes provides the

class width

Exhibit 3-5You are given the following frequency distribution.

Class

Frequency

10-14

1

15-19

2

20-24

5

25-29

8

30-34

4

Refer to Exhibit 3-5. The standard deviation is

5.477

Exhibit 1-1 In a recent study based upon an inspection of 200 homes in Daisy City, 80 were found to violate one or more city codes. Refer to Exhibit 1-1. The manager's statement that 40% of Daisy City's 2,000 homes are in violation of city codes is

only an approximation, since it is based upon sample information

When computing the mean of a set of values xi, the value of åxi

can be any value

Exhibit 3-3A researcher has collected the following sample data. The mean of the sample is 5. 3, 5, 12, 3, 2Refer to Exhibit 3-3. The range is

10

Five hundred residents of a city are polled to obtain information on voting intentions in an upcoming city election. The five hundred residents in this study is an example of a(n)

sample

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. Refer to Exhibit 6-1. The expected assembly time (in minutes) is

8

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

0.0069

Exhibit 6-9 The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of $220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed. Refer to Exhibit 6-9. Computers with prices of more than $1,750 receive a discount. What percentage of the computers will receive the discount?

0.62%

For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is

0.9267

The function that defines the probability distribution of a continuous random variable is a

probability density function

Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large university are absent on Mondays. If a random sample of 12 names is called on a Monday, what is the probability that four students are absent?

0.0683

Exhibit 6-8 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 6-8. What is the probability that a randomly selected tire will have a life of at least 30,000 miles?

0.9772

Exhibit 6-2 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-2. The probability of a player weighing less than 250 pounds is

0.9772

The weight of an object is an example of

a continuous random variable

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

0.9190

The probability density function for a uniform distribution ranging between 2 and 6 is

0.25

Variance is

a measure of the dispersion of a random variable

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

0.0558

Z is a standard normal random variable. The P(-1.5 < Z < 1.09) equals

0.7953

Given that Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1401?

0.1401

The weight of a candy bar in ounces is an example of

quantitative data

Statistical inference

is the process of drawing inferences about the population based on the information taken from the sample

Which of the following is the correct number of classes in a frequency distribution?

There is no correct number of classes.

The measure of dispersion that is influenced most by extreme values is

the range

The variance of a sample was reported to be 144. The report indicated that = 7200. What has been the sample size?

51

Exhibit 2-1 The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours

Frequency

0 - 9

20

10 - 19

80

20 - 29

200

30 - 39

100

Refer to Exhibit 2-1. The cumulative frequency for the class of 20 - 29

is 300

A tabular summary of a set of data showing the fraction of the total number of items in several classes is a

relative frequency distribution

From a population of size 400, a random sample of 40 items is selected. The median of the sample

None of these alternatives is correct.

Since a sample is a subset of the population, the sample mean

can be larger, smaller, or equal to the mean of the population

The most frequently occurring value of a data set is called the

mode

Exhibit 6-8 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 6-8. What is the probability that a randomly selected tire will have a life of at least 47,500 miles?

0.0668

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

0.5

Which of the following is NOT a characteristic of the normal probability distribution?

The standard deviation must be 1

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.119?

-1.18

Given that Z is a standard normal random variable, what is the probability that -2.08 Z 1.46?

0.9091

The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?

50%

A negative value of Z indicates that

the number of standard deviations of an observation is to the left of the mean

Z is a standard normal random variable. The P(Z > 2.11) equals

0.0174

For a standard normal distribution, the probability of obtaining a z value between -2.4 to -2.0 is

0.0146

For a normal distribution, a negative value of z indicates

the z is to the left of the mean

For the standard normal probability distribution, the area to the left of the mean is

0.5

Given that Z is a standard normal random variable, what is the value of Z if the area between -Z and Z is 0.901?

1.65

Exhibit 6-3 Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28. Refer to Exhibit 6-3. The variance of X is approximately

5.333

A continuous random variable may assume

any/all values in an interval or collection of intervals

The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages (x) in the city has the following probability distribution.

x f(x)

0 0.80

1 0.15

2 0.04

3 0.01

The mean and the standard deviation for the number of electrical outages (respectively) are

0.26 and 0.577

On a street, the houses are numbered from 300 to 450. The house numbers are examples of

categorical data

Exhibit 2-2 A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.

520/800

Refer to Exhibit 2-2. What percentage of the students does not plan to go to graduate school?

65

Exhibit 3-4 The following is the frequency distribution for the speeds of a sample of automobiles traveling on an interstate highway.

Speed Miles per Hour Frequency

50 - 54 2

55 - 59 4

60 - 64 5

65 - 69 10

70 - 74 9

75 - 79 5

35

Refer to Exhibit 3-4. The standard deviation is

7.071

Census refers to

a survey to collect data on the entire population

When a histogram has a longer tail to the right, it is said to be

skewed to the right

In a questionnaire, respondents are asked to mark their gender as male or female. Gender is an example of a

categorical variable

A graphical presentation of the relationship between two variables is

a scatter diagram

Which of the following is not a measure of central location?

variance

Social security numbers consist of numeric values. Therefore, social security is an example of

a categorical variable

The sample variance

could be smaller, equal to, or larger than the true value of the population variance

The number of customers that enter a store during one day is an example of

a discrete random variable

The variance is a measure of dispersion or variability of a random variable. It is a weighted average of the

squared deviations from the mean

Exhibit 6-6 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 6-6. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?

0.9772

Exhibit 6-10 A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. Refer to Exhibit 6-10. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course?

8.53%

Exhibit 6-10 A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. Refer to Exhibit 6-10. If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?

67.39

Exhibit 6-5 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 6-5. The probability that she will finish her trip in 80 minutes or less is

0.8

Exhibit 6-9 The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of $220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed. Refer to Exhibit 6-9. What is the minimum value of the middle 95% of computer prices?

$768.80

Which of the following is a required condition for a discrete probability function?

åf(x) = 1 for all values of x

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. Refer to Exhibit 6-1. The probability of assembling the product between 7 to 9 minutes is

0.50

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. Refer to Exhibit 6-1. The probability of assembling the product in 7 minutes or more is

0.75

For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is

0.9452

Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.9803?

-2.06

Z is a standard normal random variable. The P (-1.20 Z 1.50) equals

0.8181

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. Refer to Exhibit 6-1. The standard deviation of assembly time (in minutes) is approximately

1.1547

Exhibit 6-8 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 6-8. What percentage of tires will have a life of 34,000 to 46,000 miles?

76.98%