Final Statistics 2

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Statistics is the science of conducting studies to

collect, organize, summarize, analyze, and draw conclusion from data

is a characteristic or attribute of a subject that can assume different values

variable

Variables with values that are determined by chance are called

random variables

Inferential statistics is based on probability

True

Which of the following correctly describes the relationship between a sample and a population

A sample is a group of subjects selected from a population to be studied

Which branch of statistics would employ probability to predict how many miles one should be able to drive a 2000 Toyota Celica during its lifetime

Inferential statistics

Based on her electric bills from last year, Mrs Smith expects she will be paying $75/month this year. This is an example of descriptive statistics

False

A persons hair color would be an example of quantitative variable

False

The variable of height is an example of quantitative variables

True

The number of birds in a tree is an example of continuous variable

False

The amount of time needed to run the Boston marathon is an example of which type of variable

Continuous

Thirty students recorded the colors of their eyes, choosing from the colors brown, blue, green, hazel, and black. This data can be appropriately summarized in a

categorical frequency distribution

A recent statistics exam yielded the following 25 scores. Construct a frequency distribution with the class limits shown below. (68,81,75,56,62,59,83,70,66,93,81,81,46,75,87,77,89,80,97,59,75,75,47,85,98)

Class Limits Tally Frequency
41-50 II(2) 2/25
51-60 III(3) 3/25
61-70 IIII(4) 4/25
71-80 IIIIII(6) 6/25
81-90 IIIIIIII(8) 8/25
91-100 II(2) 2/25

A recent statistics exam yielded the following 10 scores. Construct a frequency polygon distribution using the class limits shown below

Class Limits/Midpoints/Tally/Frequency
61-70 65.5 II 2
71-80 75.5 IIII 4
81-90 85.5 II 2
91-100 95.5 II 2
Line graph

Find the class with the least number of data values

85-95

Which of the following could be a cumulative frequency graph

when the graph goes up in a positive way

Which of the following is a histogram

the one that is a bar graph with bars touching

Which type of graph represents the data by using vertical bars of various height to indicate frequencies

Histogram

Given the following frequency distribution, how many pieces of data were less than 28.5
Class Boundaries/Frequencies
13.5-18.5/4
18.5-23.5/9
23.5-28.5/12
28.5-33.5/15
33.5-38.5/17

25

What type of graph below with bars together and in order from largest to smallest

Pareto Chart

Find the mean of the given data (7,8,9,10,11)

9.7

What is the median of the following set of values (8,6,3,1,12)

6

Find the mode for the following data (5,4,3,4,5,6,5,5,3,4)

5

What is the mid range of the following data set. (3,9,8,10,2,10,16,16,16)

9

Find the mean of the following data set (11,6,9,4,15)

9

What is the median of the following data set (7,10,14,15,19)

14

The number of police officers in selected city districts is listed below. Find the mode (24,26,24,30,23,28,19,31,24,26,19)

24

Find the mean, median, mode for following data set (12,15,18,18,15,22,15,30,12)

Mean 17.4
Median 15
Mode 15
Mid-range 21

Find the mean of the following set of values (0,7,5,3,5)

4

Find the median of the following data set (4,11,8,7,4)

7

Find the median for the following data (6,7,4,5,3,7,4)

5

What is the mean of the following data set (8,12,15,16,17)

13.6

What is the median of the following set of values (6,20,18,14,18,13,14,18)

16

What is the mode of the following data set (8,22,20,16,20,18,15)

20

Find the mean of the following data set (9,11,11,11,9,15)

11

Find the median of the following data set (5,7,7,7,5,11)

7

If a distribution is negatively skewed as shown in the figure below the mean will fall to the left of the median

False

In a unimodal, symmetrical distribution as shown in the figure below

The mean, the median, and mode are the same

the median can be a more appropriate measure of central tendency if the distribution of the data is extremely skewed

True

is the midpoint in a data array

median

the ,,,,, and ,,,, are two measures of variation used to describe the spread of the data in a data set

variance and standard deviation

Determine the range for the following data set (4,7,3,16,5,22,8)

19

Given that the variance for a data set is 1.20 what is the standard deviation

1.1

Given that the mean of a set of data is 25 and the standard deviation is 3, what is the coefficient of variation

12%

If a student scored 89 points on a test where the mean score was 80.2 and the standard deviation was 4.7 the students z score is

1.87

Indicate which student has the higher z score
Art major X=46 x̄=50.5 s=5.2
Theater major X=70 x̄=75.1 s=7.3

The theater major has a higher score than the art major

A baseball player has a batting average of 0.325 each week of the season, with a standard deviation of 0.065 what is the z score when he bats 0.410 one week

1.308

Check the following data set for outliers (73, 82, 84,84,86,87,89,91)

73 is an outlier q1=83 q3=88 lower limit 75.5 upper limit 95.5

Identify the five number summary of the following data set (7,11,21,28,32,33,37,43)

7,16,30,35,43

A five number summary of a data set consists of the minimum q1 the median q3 and the maximum

True

What is the set of all possible outcomes of a probability experiment

The sample space

If the probability that it will rain tomorrow is 0.31 what is the probability that it will not rain tomorrow

0.69

If there are 11 equally likely events then the probability of the first one occurring is 1/11

True

Find the probability of getting a number of greater than 5 when a die is rolled one time

1/3

If two dice are rolled one time, find the probability of getting a sum of 6

5/36

If two dice are rolled one time find the probability of getting a sum less than 5

1/6

If a red suit is drawn from an ordinary deck of cards what is the probability that the card is a diamond

1/2

At Wassamatta University 52.3% of the student body are males choose one student at random what is the probability that the student is female

47.7%

In a recent study the following response were obtained to the question, "do you favor recycling in your neighborhood" Males Yes 25 No 15 No Opinion 10 Female Yes 30 No 10 No Opinion 10 If a response is picked at random what is the probability that it came from a male or that it indicated no opinion regarding recycling

3/5

Box A contains the number 1,2,3,4, Box B contains the numbers 5,6,7,8. A number is first drawn from Box A and then another number from Box B using the figure below how many outcomes are possible if both numbers are even

4

If a single card id drawn from an ordinary deck of cards what is the probability of drawing a jack queen king or ace

4/13

An apartment building has the following distribution of apartments
1 bedroom 2 bedroom 3 bedroom
1st floor 3 1 1
2nd floor 2 2 2
3rd floor 1 4 1

11/17

The statistics club at woodvale college sold college T's as a fundraiser. The results of the sale are shown below. Choose one student at random. Find the probability that the student sold 11-15 shirts or less than 6 T's
No of T-shirts No of Club Members
0 1
1-5 15
6-10 13
11-15 3
16-20 6
20+ 1

0.4872

If a card is drawn from an ordinary deck of cards and then a second card is drawn from the same deck without replacing the first card these two events are

dependent

A recent poll found that 30% of those surveyed are worried about aggressive drivers on the road. If three people are selected at random, what is the probability that all three will be worried about aggressive drivers on the road

0.027

In a second grade class containing 12 girls and 10 boys, 2 students are selected at random to give out the math papers what is the probability that both are girls?

4/7*11/20

If five cards are drawn from a deck of cards without replacement, what is the probability that at least one of the cards is a heart

0.778

A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, find the probability that both are statistics books.

1/21

The following distributions is not a probability distribution because (0.16, 0.15, 0.43, 0.16, 0.24)

The probability values do not add to 1

The following distribution is not a probability distribution because(0.22, 0.21, -0.26, 0.53, 0.30)

A probability is negative

Find the mean of the distribution shown (x:1,2; p(x):0.37, 0.63)

1.63

Find the mean of the distribution shown below (x:2,3,4; p(x):0.38, 0.36, 0.26)

2.88

Find the mean of the distribution shown (x: 4,6; p(x):0.30, 0.70)

5.40

In a large bag of marbles, 20% of them are red. A child chooses 4 marbles from this bag. If the child chooses the marbles at random, what is the chance that the child gets exactly three red marbles

0.026

A student takes a 15 question multiple choice exam with three choices for each question and guesses on each question find the probability of guessing exactly 3 out of 15 correctly

0.130

A pet supplier has a stock of parakeets of which 40% are blue parakeets A pet store orders 3 parakeets from this supplier. If the supplier selects the parakeets at random, what is the chance that the per store gets exactly one blue parakeet

0.432

A school is sending 16 children to a camp. If 25% of the children in the school are first graders and the 16 children are selected at random from among all 6 graders at the school, find the mean and variance of of the number of first graders chosen

The mean is 4.0 and the variance is 3.0

A computer store has 75 printers of which 40 are laser printers and 35 are ink jet printers. If a group of 10 printers is chosen at random from the store, find the mean and variance of the number of ink jet printers.

Mean 4.7 variance 2.5

A die is rolled 360 times find the standard deviation of the number of times a 3 will be rolled

7.1

In a survey, 75% of the voters support a particular referendum. If 20 voters are chosen at random, find the mean and variance for the number of voters who support the referendum.

the mean is 15 and the variance is 3.75

The failure rate for taking the bar exam in Philadelphia is 41%. If 375 people take the bar exam , what is the mean for the number of failures?

153.8

If a gambler rolls two dice and gets a sum of 10, he wins $10 and if he gets a sum of three he wins $20. The cost to play the game is $5 What is the expectations of this game.

-$3.06

Identify the type of distribution pattern that occurs when the majority of the data values fall to the left of the mean

positively skewed

Which of the following characteristics does no apply to a theoretical normal distribution

It is bimodal

For a normal distribution curve with a mean of 17 and a standard deviation of 4 which range of the variable defines an area under the curve corresponding to a probability of approximately 68%

from 13-21

What is the area under the standard normal distribution curve between z=1.50 and z=2.50

0.0606

Find the probability P(0<z<1.67), using the standard normal distribution

45.25%

Find the probability P(0.21<z<1.28) using the standard normal distribution

0.3166

If a normally distributed group of test scores have a mean of 70 and standard deviation of 12 find the percentage of scores that will fall below 50

4.75%

At a large department store, the average number of years of employment for a cashier is 5.7 with a standard deviation of 1.8 years and the distribution is approximately normal. If an employee is picked at random what is the probability that the employee has worked at the store for over 10 years

0.8%

the average hourly wage of workers at a fast food restaurant is $6.50/hr. Assume the wages are normally distributed with a standard deviation of $0.45. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $6.75

28.8%

A recent study found that the life expectancy of a people living in Africa is normally distributed with an average of 53 years with a standard deviation of 7.5 years. If a person in Africa is selected at random what is the probability that the person will die before the age of 65

94.5%

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