Deck 26: Introduction to Statistics and Probability

Question 1

Define the following type of data as continuous, discrete, or categorical: The time it takes to drive from one city to another.

Answer 1

Continuous

Question 2

The following table shows the number of computers (in millions) sold in the years 1996-2010: Make an x-y graph of the sales versus the year.

Answer 2

Question 3

Define the following type of data as continuous, discrete, or categorical: The number of times a person dines out at a restaurant (per month).

Answer 3

Discrete

Question 4

Company $x$ sold 127 computers in the year 1990. The number of computers sold by each of its five sales representatives in 1990 is shown in the table below:

(a) Make a bar chart for the data.
(b) Make a pie chart for the data.

Question 5

Define the following type of data as continuous, discrete, or categorical: Time spent watching television each week

Question 6

Use the information below for questions.
The average monthly rainfall (cm) in several cities in a certain province are:

$\begin{array}{lllll} 11.3 && 29.6 && 16.3 && 31.4 && 29.2 && 14.5\\ 16.9 && 25.8 && 21.3 && 32.7 && 15.3 && 13.5\\ 25.2 && 22.5 && 18.6 && 14.3 && 26.9 && 22.9 \end{array}$

-(a) Determine the range of the data.
(b) Make an absolute frequency distribution using class widths of $2.5 \mathrm{~cm}$ .
(c) Make a relative frequency distribution using class widths of $2.5 \mathrm{~cm}$ .

Question 7

Use the information below for questions.
The average monthly rainfall (cm) in several cities in a certain province are:

$\begin{array}{lllll} 11.3 && 29.6 && 16.3 && 31.4 && 29.2 && 14.5\\ 16.9 && 25.8 && 21.3 && 32.7 && 15.3 && 13.5\\ 25.2 && 22.5 && 18.6 && 14.3 && 26.9 && 22.9 \end{array}$

-Draw a histogram, showing both absolute and relative frequencies.

Question 8

Use the information below for questions.
The average monthly rainfall (cm) in several cities in a certain province are:

$\begin{array}{lllll} 11.3 && 29.6 && 16.3 && 31.4 && 29.2 && 14.5\\ 16.9 && 25.8 && 21.3 && 32.7 && 15.3 && 13.5\\ 25.2 && 22.5 && 18.6 && 14.3 && 26.9 && 22.9 \end{array}$

-Draw a frequency polygon showing both absolute and relative frequencies.

Question 9

Use the information below for questions.
The average monthly rainfall (cm) in several cities in a certain province are:

$\begin{array}{lllll} 11.3 && 29.6 && 16.3 && 31.4 && 29.2 && 14.5\\ 16.9 && 25.8 && 21.3 && 32.7 && 15.3 && 13.5\\ 25.2 && 22.5 && 18.6 && 14.3 && 26.9 && 22.9 \end{array}$

-Make a cumulative frequency distribution, showing (a) absolute frequency and (b) relative frequency.

Question 10

Use the information below for questions.
The average monthly rainfall (cm) in several cities in a certain province are:

$\begin{array}{lllll} 11.3 && 29.6 && 16.3 && 31.4 && 29.2 && 14.5\\ 16.9 && 25.8 && 21.3 && 32.7 && 15.3 && 13.5\\ 25.2 && 22.5 && 18.6 && 14.3 && 26.9 && 22.9 \end{array}$

-Draw a cumulative frequency polygon, showing both absolute and relative frequencies.

Question 11

The amount of hours spent on the computer per week for a sample of 40 random people is given below:
$\begin{array}{cccccccccc} 3 & 3 & 5 & 5 & 7 & 7 & 7 & 8 & 10 & 10 \\ 10 & 12 & 12 & 13 & 14 & 14 & 14 & 14 & 15 & 15 \\ 15 & 15 & 15 & 16 & 17 & 18 & 18 & 18 & 20 & 21 \\ 21 & 21 & 21 & 21 & 22 & 23 & 25 & 25 & 25 & 28 \end{array}$
(a) Construct a frequency distribution for the data (include class, frequency, and cumulative relative frequency).
(b) Draw a histogram for the distribution.

Question 12

The time (in minutes) taken to commute to work for 24 random people is given below:
$\begin{array}{cccccccc} 5 & 7 & 8 & 8 & 10 & 10 & 12 & 15 \\ 15 & 15 & 18 & 20 & 20 & 20 & 20 & 22 \\ 24 & 24 & 25 & 25 & 25 & 26 & 27 & 28\end{array}$
Construct a frequency distribution for the data (include class, frequency, and cumulative relative frequency).

Question 13

Consider the below set of lengths for questions:

$\begin{array}{l} 123 && 422 && 566 && 329 && 247 && 296 && 245 && 522\\ 362 && 593 && 229 && 475 && 357 && 227 && 489 && 326 \end{array}$
-Find the mean of the lengths.

Question 14

Consider the below set of lengths for questions:

$\begin{array}{l} 123 && 422 && 566 && 329 && 247 && 296 && 245 && 522\\ 362 && 593 && 229 && 475 && 357 && 227 && 489 && 326 \end{array}$
-Find the median of the lengths.

Question 15

Consider the below set of lengths for questions:

$\begin{array}{l} 123 && 422 && 566 && 329 && 247 && 296 && 245 && 522\\ 362 && 593 && 229 && 475 && 357 && 227 && 489 && 326 \end{array}$
-Find the mode of the lengths.

Question 16

Consider the below set of lengths for questions:

$\begin{array}{l} 123 && 422 && 566 && 329 && 247 && 296 && 245 && 522\\ 362 && 593 && 229 && 475 && 357 && 227 && 489 && 326 \end{array}$
-Find the range of the lengths.

Question 17

Consider the below set of lengths for questions:

$\begin{array}{l} 123 && 422 && 566 && 329 && 247 && 296 && 245 && 522\\ 362 && 593 && 229 && 475 && 357 && 227 && 489 && 326 \end{array}$
-Find the quartiles and find the quartile range of the lengths.

Question 18

Consider the below set of lengths for questions:

$\begin{array}{l} 123 && 422 && 566 && 329 && 247 && 296 && 245 && 522\\ 362 && 593 && 229 && 475 && 357 && 227 && 489 && 326 \end{array}$
-Find the sample variance and standard deviation of the lengths.

Question 19

Determine the quartiles and give the quartile range of the data: $211,226,228,240,256,292,310,376$ , $384,402,421$

Question 20

The heights (in centimeters) of 35 students at Hatfield College are given below:
$157.5, 142.2, 172.7, 165.1, 165.1, 177.8, 180.3, 165.1, 167.6, 180.3,\\162.6, 182.9, 147.3, 152.4, 157.5, 162.6, 172.7, 185.4, 155.0, 167.6,\\170.2, 177.8, 170.2, 175.3, 167.6, 190.5, 175.3, 160.0, 172.7, 160.3,\\165.1, 172.7, 175.3, 165.1, 162.6$
(a) Determine the range of the data.
(b) Make a frequency distribution using class widths of $8 \mathrm{~cm}$ . Show both absolute and relative frequencies.
(c) Draw a frequency polygon showing both absolute and relative frequencies.
(d) Make a cumulative frequency distribution. Show both absolute and relative frequencies.
(e) Find the mean.
(f) Give the 5-number summary (minimum, $1^{\text {st }}$ quartile, median, $3^{\text {rd }}$ quartile, maximum).
(g) Find the standard deviation. Assume that the heights are a sample drawn from a larger population.

Question 21

What is the arithmetic mean of the following sample of weights of Lake Ontario in kilograms.
$1.7,2.1,1.3,0.7,1.7,1.5,1.3,2.0,1.9$

Question 22

The amount of hours spent on homework and studying per week for a sample of 30 random students is given below:
$\begin{array}{cccccccccc} 3 & 5 & 6 & 6 & 7 & 7 & 7 & 7 & 8 & 8 \\ 9 & 10 & 10 & 12 & 13 & 14 & 14 & 14 & 15 & 15 \\ 17 & 19 & 20 & 20 & 21 & 21 & 24 & 27 & 28 & 30 \\ \end{array}$
(a) Find the mean.
(b) Find the median.
(c) Find the mode.
(d) Find the range.
(e) Find the standard deviation to three significant digits.

Question 23

From a random sample of 100 cars, the following data on the number tires that need replacing was found:
$\begin{array}{|c|c|}\hline Number of Tires & Frequency \\\hline 0 & 10 \\\hline 1 & 25 \\\hline 2 & 42 \\\hline 3 & 19 \\\hline 4 & 4 \\\hline\end{array}$
Find the weighted mean.

Question 24

The amount of texts sent per day for a sample of 10 random people is given below:
$\begin{array}{lllll}5 & 10 & 25 & 25 & 40 \\50 & 60 & 75 & 100 & 120 \\\end{array}$
(a) Find the mean.
(b) Find the median.
(c) Find the mode.
(d) Find the range.
(e) Find the standard deviation to three significant digits.

Question 25

A bag contains five yellow jelly beans, six red jelly beans and eight blue jelly beans. If a jelly bean is drawn at random from the bag, what is the probability that it will be red?

Question 26

In a certain parking lot, $45 \%$ of the cars have four doors, $16 \%$ of the cars are blue, and $4 \%$ of the cars have four doors and are blue. What is the probability that a car chosen at random will have either four doors or a blue color, or both?

Question 27

If we throw two dice, what is the chance that their sum is 11 ?

Question 28

We draw a ball from a bag that contains 4 red balls and 11 white balls. We replace the ball and draw another ball. What is the probability that both balls are white balls?

Question 29

Find the probability that a card drawn from a deck will be either a four or a diamond.

Question 30

If a die is rolled seven times, what is the probability of obtaining exactly three sixes?

Question 31

If you flip a coin and roll a die, what is the probability of obtaining a heads on the coin and a three or four on the die?

Question 32

In "old school" Dungeons and Dragons game, you might find that for your character to defend against an attack, you have to roll 17 or higher on a 20 -sided die. What is the probability of defending against three attacks in a row?

Question 33

In testing the thickness of a protective coating sprayed onto metal plates, there is a $88 \%$ probability that a single plate selected at random will pass inspection. What is the probability that of 15 plates sampled, 12 will pass inspection?

Question 34

In a cell phone transmission tower there is a 0.002 probability of an intermittent power short circuit and a 0.01 probability of a faulty fuse. What is the probability of a short circuit or faulty fuse or both occurring? Assume that a short circuit and a faulty fuse occur independently.

Question 35

A box contains twelve $5 \mathrm{amp}$ fuses and eight $10 \mathrm{amp}$ fuses. What is the probability of selecting a $10-$ amp fuse at random?

Question 36

Rolling two standard six-sided dice, what is the probability of rolling a sum of 10 ?

Question 37

A certain coffee company has a prize promotion involving peeling a sticker from the top of your cup. If one in eight cups is a winner, what is the probability of winning 4 times if you buy 20 coffees? Express your answer to four decimal places.

Question 38

A factory claims a $4 \%$ defective rate on items produced. If a quality control engineer samples 25 items, what is the probability that 3 are defective? Express your answer to four decimal places.

Question 39

We draw a ball from a bag that contains 5 red balls and 8 blue balls. We set aside the ball and draw another ball. What is the probability that both balls are blue balls?

Question 40

What is the probability of a sum of 6 when rolling 3 standard six sided dice?

Question 41

Find the area under the normal curve between the mean and 1.7 standard deviations. Use a table of area under the curve within $z$ standard deviations of the mean.

Question 42

The distribution of grades on a certain test has a mean of 85.5 with a standard deviation of 11.2. There are 400 tests. Assuming that the grades are normally distributed, predict the number of students scoring between 75 and 95 . Use a table of area under the curve within $z$ standard deviations of the mean.

Question 43

Find the area under the normal curve between 1.2 standard deviations on both sides of the mean.

Question 44

On a test given to 150 students, the mean grade was 74.2 with a standard deviation of 9.8. Assuming a normal distribution, estimate the number of $B$ grades (between 80 and 90).

Question 45

In a normal distribution, the mean is 85 , and the standard deviation is 12 . For a single value, a z-score is 1.3. What is the value?

Question 46

A particular beverage company states that the volumes of the bottles they produce are normally distributed with a mean of $2000 \mathrm{~mL}$ and a standard deviation of $10 \mathrm{~mL}$ . What is the probability that a randomly sampled bottle has a volume more than $2015 \mathrm{~mL}$ .

Question 47

A snack company states that the weight of their chip bags is normally distributed with a mean of $180 \mathrm{~g}$ and standard deviation of $5 \mathrm{~g}$ . What is the probability of a randomly selected chip bag having a weight less than $170 \mathrm{~g}$ ?

Question 48

A certain circuit has a resistance that is normally distributed with a mean of $25.0 \Omega$ and a standard deviation of $1.0 \Omega$ . What is the probability of circuit having a resistance between $23.2 \Omega$ and $24.6 \Omega$ ?

Question 49

The amount of caffeine in a cup of coffee is normally distributed with a mean of $95.0 \mathrm{mg}$ and a standard deviation of $10.0 \mathrm{mg}$ . What amount of caffeine will $5 \%$ of coffee will have less caffeine than?

Question 50

A local refinery produces an amount of oil that is normally distributed with a mean of 250000 barrels per day with a standard deviation of 25000 barrels per day. What is the probability that the refinery will produce more than 300000 barrels on a given day?

Question 51

The speeds of 180 randomly chosen cars passing a certain point on a highway were measured. The mean was found to be $104.2 \mathrm{~km} / \mathrm{h}$ and their standard deviation was $6.1 \mathrm{~km} / \mathrm{h}$ . Estimate the mean speed of the entire population of cars with a confidence level of $95 \%$ .

Question 52

A single sample of size 64 drawn from a population is found to have a mean of 135 and a standard deviation of 8.3. Estimate the population mean with a confidence level of $68 \%$ .

Question 53

In a sample of 850 ring bearings, the standard deviation is $0.02 \mathrm{~mm}$ . What is the Standard Error of the sample?

Question 54

A random survey of 100 people asking the number of cups of coffee they drank per week found a mean of 8 with standard deviation of 2.5 . Find the $68 \%$ confidence interval for the population mean.

Question 55

A random sample of 400 students found that $70 \%$ are currently enrolled in a mathematics course. Find the $95 \%$ confidence interval for the population proportion.

Question 56

A random sample of 60 new cars found a mean cost of $\$ 27,500$ with standard deviation of $\$ 4750$ . Find the $68 \%$ confidence interval for the population mean.

Question 57

A random survey of 80 students found they spent a mean of 21 hours in class per week with standard deviation of 3 hours per week. Find the $95 \%$ confidence interval for the population mean.

Question 58

A random sample of 500 parts found 20 to be defective. Find the 95% confidence interval for the population proportion.

Question 59

The proportion defective for samples of 200 calculators per day for 20 days as follows: Find the mean proportion defective and the values of the upper and lower control limits.

Question 60

Five pieces of tubing are taken from a production line each day for 20 days and the lengths are measured. Their lengths, in $\mathrm{cm}$ , are as follows:

Find the values of the central line and upper and lower control limits for the mean.

Question 61

For the table in problem 60 , find the average range $\bar{R}$ , and determine the upper and lower control limits for the range.

Question 62

A factory kept track of its defectives (from random samples of 500 ) for 10 days and the following data was found:
Find the values for the central line, and determine the upper and lower control limits.

Question 63

A factory kept track of its defectives (from random samples of 400 ) for 10 days and the following data was found:
Find the values for the central line, and determine the upper and lower control limits.

Question 64

Find the correlation coefficient and the least squares line for the following data:

Question 65

The weight of a tray of $11 \mathrm{~mm}$ hex bolts and the number of bolts on the tray will have what correlation coefficient?

Question 66

The temperature of a metal casting set out to cool was recorded over time and the following data was found:
Find the correlation coefficient and the least squares line.

Question 67

Given the following data:
Find the correlation coefficient and the least squares line.

Question 68

The amount of honey in a bee hive was recoded over several days
Find the correlation coefficient and the least squares line.