MBA 513 mod 2 ch4&7

Which of the following is the correct formula to standardize a value?

(Original value - Mean)/Standard deviation

A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 400 and 500?

0.2139 Reason: z=(400-560)/90=-1.78; z=(500-560)/90=-0.67. Use Excel function Normdist or z-tables (0.4625-0.2486). we subtracted. 560 is not in range

Scores on a graduate school entrance exam follow a normal distribution with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen test taker will score between 490 and 560?

0.2823 Reason: z=(490-560)/90= -0.78. Use Excel function Normdist or z-tables (0.5 - 0.2177 = 0.2823).

Scores on a graduate school entrance exam follow a normal distribution with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen test taker will score between 560 and 640?

0.3133 Reason: z=(640-560)/90=0.89. Use Excel function Normdist OR z-tables (0.3133).

What would the location of the 83rd percentile be for a data set with 40 observations?

34.03 LP = (n +1) p/100 L83 = (40 + 1) 83/100 = 34.03

3/4

3rd quartile

For the following ordered set of data, find the 40th percentile. 0, 2, 4, 5, 5, 6, 7, 7, 8

5 REASON: Lp= (n +1) p/100 L40 = (9 +1) 40/100 = 4 Locate the fourth value in the ordered array.

4/5

8th decile

For data that is normally distributed, the percentage of the data that falls within two standard deviations of the mean is ______.

95%

Choose the statement that best describes a scatter diagram.

A graphical technique to show the relationship between two variables,

A dot plot would be appropriate to display which one of the following kinds of data?

A small set of data.

For a given data set, suppose Q1 = 70, Q2 = 80, Q3 = 100. Which of the following is true about outliers?

An observation of 20 would be an outlier.

If a random variable is normally distributed, what percentage of the observations will lie within plus and minus 1 standard deviation of the mean?

Approximately 68%

CH 7 Which of the following is true regarding continuous and discrete random variables.

Continuous random variables usually result from measuring.

Which one of the following pairs of variables would be best-suited for a contingency table? -Hours Studied and Test Grade -Miles per gallon and Car Weight -Size of House and Price of House -Favorite Color and Gender

Favorite Color and Gender reason: not a number

The interquartile range is the difference between which two quartiles?

First and third reason: IQR = Q3 - Q1

Which of the following statements is MOST accurate?

For data that is normally distributed, 95% of the data will fall within two standard deviations of the mean.

How would you describe the shape of the Normal Distribution?

It is "bell" shaped, and symmetrical with the center at μ.

Where does the curve of the normal distribution touch the x-axis?

It never touches, but approaches asymptotically in both directions.

Choose the correct formula for the location, Lp ,from n observations where P is the desired percentile.

Lp = (n+1) p over 100

What are the upper and lower limits of the random variable for the Normal distribution?

No limits. It is asymptotic in both directions.

Contingency tables are used for summarizing data of what level?

Nominal Ordinal

Which one of the following formulas is Pearson's Coefficient of Skewness?

SK = 3 ( X - median) / S (all over s)

Separates the bottom 50% of the data from the upper 50%

Second Quartile

Since the normal probability distribution is symmetrical about the mean, which of the following is true?

The area on each side of the mean is 0.5.

If a set of data exhibits significant positive skewness, then which of the following would be expected of Pearson's coefficient of skewness?

The coefficient should be close to 3. reason: The coefficient must be between -3 and 3 -Coefficients close to 0 indicate symmetrical distributions. -Coefficients less than 0 indicate negative skewness.

Which one of these statements is not part of the description of a scatter diagram? -Each observation is measured with two variables. -It may show a relationship or lack of relationship between two variables. -One variable is scaled on the horizontal axis, the other on the vertical axis. -The data points are connected to create a graph.

The data points are connected to create a graph.

Which is the best definition of the z-value?

The distance between a value x and the mean, μ, divided by the standard deviation, σ

Suppose a given data set has the following characteristics: Minimum value: 120 Q1: 160 Q2: 190 Q3: 200 Maximum Value: 220 Which of the following is true about the distribution of the data?

The distribution is negatively skewed. Reason: (its NOT positively skewed) The minimum is not closer to the median than the maximum. Q1 is not closer to the median than is Q3. Reason: (its NOT symmetrical) The minimum and maximum values are not the same distance from the median. Q1 and Q3 are not the same distance from the median.

Which one of the following is a result of the normal probability distribution being bell-shaped?

The mean, median, and mode are at the center.

A box plot is constructed using several different values. Which of the following values are included in a box plot

The smallest value The second quartile The third quartile

Dot plots allow one to observe which of the following?

The spread in a distribution. The shape of a distribution. The center of a distribution.

Which of the following is an example of a continuous random variable?

The square footage of a house.

For a given data set, suppose Q1 = 40, Q2 = 45, Q3 = 50. Also, suppose that the three smallest observations are 20, 24, and 28. Which of the following is true about the box plot for this data set?

There would be two asterisks plotted to indicate outliers at 20 and 24. Reason: An outlier is the value less than 25, found by Q1 - 1.5(Q3 - Q1) 40 - 1.5(50 - 40) 40 - 15 = 25 Therefore, observations 20 and 24 are outliers

Separates the bottom 75% of the data from the upper 25%

Third Quartile

What is the function of "quartiles"?

To divide a set of observations into four equal parts

The average height for an American male is 71 inches and the standard deviation is 3 inches. What is the z-value for a height of 68 inches?

Z = -1 reason: X - μ / σ 68 - 71 / 3 = -1

A statistic that indicates the direction and the strength of the relationship between two variables and ranges from -1.00 to +1.00 is

a correlation coefficient.

A statistic that indicates the direction and strength of the relation between two variables is known as a correlation ___________

coefficient

100 percentiles 10 deciles 4 quartiles 2 median

correct

sk=1.83 : Moderate positive skewness sk=0.01 : very nearly symmetrical sk=-1.52 : Moderate negative skewness sk=2.60 : Large positive skewness

correct

Separates the bottom 25% of the data from the upper 75%

first quartile

A z value is a distance from the _____________, measured in units of the standard deviation.

mean

1/2

median

A value that is considerably larger or smaller than most of the values in a data set is called a(n)

outlier

An outlier is a value that is more than 1.5 times the interquartile range ______

smaller than the first quartile. larger than the third quartile.

Which of the following is not a measure of position? ninth decile first quartile 90th percentile standard deviation

standard deviation

to ____________ the data, one should rescale each type of data so that it measures the number of standard deviations above or below the mean for a standard normal distribution.

standardize

The length of the interval that contains the middle 50% of measurements is known as ______.

the interquartile range

Bivariate data is data that has ______ variable(s) and thus can be displayed on a scatterplot. Univariate data is data that has _____ variable(s), so it cannot be displayed on a scatterplot.

2 1

1/5

20th percentile

What do we mean when we say there is a "family" of normal distributions?

-A single equation describes all normal distributions. -Distributions may have different means and standard deviations but still be "normal" in shape.

Which of the following statements describe a feature of a scatter diagram?

-Each paired observation is represented by a single dot -One variable is scaled on the horizontal axis and the other is scaled on the vertical axis

Which of the following are features of a dot plot?

-One dot for each observation. -A horizontal line indicating the possible values of the data. -Dots "piled up" for observations very close together.

When you create a dot plot, you do which of these operations?

-Place a dot along a horizontal scale for each observation. -"Pile up" dots that are too close to show separately.

Which of the following statements are true about the symmetric characteristic of the normal probability distribution?

-The area on each side of the mean equals one-half. -The shape to the left of the mean is a mirror image of the shape to the right of the mean.

Which of the following statements are true with respect to both the Standard Normal distribution and any normal probability distribution?

-The areas are equal to 1. -A normal probability distribution can be converted into a standard normal distribution.

Suppose you have two normal distributions: one has μ = 16 and σ = 2 and the other has μ = 20 and σ = 3. Which of the following statements are true?

-The distribution with μ = 20 is to the right of the other distribution. -The distribution with σ = 2 is more peaked.

Approximately 68%

μ ± σ (within one standard deviation of the mean)

The average weight of a Honeycrisp apple is 110 grams and the standard deviation is 20 grams. What is the z-value for an apple that weighs 140 grams?

1.5 REASON: z = 140 - 110 / 20 = 1.5

Which of the following statements are true of the Standard Normal Distribution?

-The mean (μ) is zero. -The standard deviation (σ) is 1

Each of the following is a measure of position in a set of data except: the median the deciles the quartiles the standard deviation

the standard deviation

Which of the following formulas is used to convert a normally distributed random variable, X, to a z-value?

z = X - μ / σ

Approximately 95%

μ ± 2σ (within two standard deviation of the mean)

Approximately 99.7%

μ ± 3σ (within three standard deviation of the mean)

A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 600 and 700?

0.2706 Reason: z=(600-560)/90=0.44; z=(700-560)/90=1.56. Use Excel function Normdist or z-tables (0.4406-0.1700). we subtracted bc 560 is not in the range

Applicants for graduate school take a test that has scores which are normally distributed with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen applicant will score between 550 and 650?

0.3851 Reason: z=(550-560)/90=-0.11; z=(650-560)/90=1.00. Use Excel function Normdist or z-tables (0.3413+0.0438).

Applicants for graduate school take a test that has scores which are normally distributed with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen applicant will score between 500 and 600?

0.4186 Reason: z=(500-560)/90=-0.67; z=(600-560)/90=0.44. Use Excel function Normdist or z-tables (0.2486+0.1700) we added bc 560 is within the range ?

For the following ordered set of data, find the 60th percentile. 0, 2, 3, 5, 5, 6, 8, 10, 10, 11, 12, 14, 16

10 REASON: lp = (n+1) p/100 l60 = (13 + 1) 60/100 = 8.4 The 60th percentile is 40% of the way from the 8th observation to the 9th observation. Since the 8th and 9th observations are the same, the 60th percentile is 10.