Annick wanted to compare her height to the rest of the students of her school. There are
480 students who have been measured, including her. Seventy percent (70%) of the
students are shorter than Annick and she is in the 10% of students who are 1.6 metres tall.
Calculate the percentile ranking of Annick’s height.
The Manitoba Chamber of Commerce will give an award to the top 10 percent of
companies in the area of customer satisfaction. ManCrete Construction satisfies 95% of its
customers. Justify whether ManCrete Construction will be given an award this year.
Marvin Batteries conducted a study on the life expectancy of its car batteries. It found the
data to be normally distributed. Part of the information is provided below:
A) State the mean and standard deviation of the data. (1 mark)
B) If this company produces 100 000 batteries a year, how many will last between
6 and 7 years? (1 mark)
C) During the course of the study, Marvin Batteries noticed that one of its batteries had a
life span of 15 years. Using your knowledge of the normal curve, explain how this is
possible. (1 mark)
At a swim competition, 100 swimmers swam the 50-metre freestyle. A computer program
printed the data for the race. It stated:
Find the standard deviation of the data.
The diagram below shows the relationship between a person’s arm span and his or her
A) Based on the data presented, what can be concluded about the relationship between
arm span and height? (0.5 mark)
B) Provide an approximate “r-value” that represents the relationship between arm span
and height. (0.5 mark)
Eighty-five (85) people ran in a marathon. Parminder finished alone in 22nd place.
Calculate Parminder’s percentile ranking.
Marty achieved 79% on his last test and was in the 79th percentile rank. Marty’s teacher
increased each student’s mark by 1%. Marty now has 80% and tells his friend Carl that he
is now ranked in the 80th percentile. Carl disagrees.
Identify who is correct and justify your answer.
A manufacturer produces MP3 players with a life expectancy that follows a normal
distribution. The mean life expectancy is 5 years and the standard deviation is 0.75 year.
A) Find the percent of MP3 players that last fewer than 3.5 years. (1 mark)
B) If 220 000 MP3 players are manufactured in a particular year, find the number of
MP3 players with a life expectancy greater than 5.75 years. (1 mark)
For each of the following situations, state whether their correlation coefficient would be
positive, negative, or zero.
A) First four years of a new car’s value versus time. (0.5 mark)
B) Cost of a home versus size. (0.5 mark)
There is a positive correlation between the number of hours one studies for an English test
and the mark earned. The r-value is 0.75.
A) Sketch a scatter plot of this correlation using approximately 10 dots. (1 mark)
B) Suppose that the r-value of the given scenario was r = 1. Sketch a scatter plot using a
minimum of 5 dots. (1 mark)
A survey of students was conducted to determine their average yearly income. The
results are summarized in the table below:
What percent of students earned an average yearly income of $4 000?
Lovepreet and her classmates did fundraising for the United Way. Lovepreet raised more
money than 34 of her friends, and the same amount as 2 friends. Calculate Lovepreet’s
percentile rank if there were 43 classmates involved in the effort.
A class of students wrote a quiz that had 20 multiple-choice questions. Pedro was in
the 80th percentile rank and scored 75%. How many questions did he get right?
A coach collected data on the weight of his football team and found the weight to be
A) State the mean and standard deviation of the data. (1 mark)
B) The team has 50 players during the season. How many weigh less than 117 kg?
The attendance records of six students were collected, along with their final marks in the
A) Graph the data from the chart above. (1 mark)
B) Identify the type of correlation present. (0.5 mark)
Listed below are 24 students’ math scores.
Determine which score is Rob’s if his percentile rank on the math test is 58.
The correlation coefficient (r-value) is a number that falls between –1 and +1.
The mean driving speed on Manitoba highways is 102 km/h. The speed is normally
distributed with a standard deviation of 3 km/h.
A) Calculate the percent of people who drive between 99 and 108 km/h. (0.5 mark
B) Out of 1 000 vehicles on a highway, how many will be driven faster than 105 km/h?
At the end of the basketball season, Bob Slammer and Jim Missalot had scored the same
number of points. The standard deviation for points scored per game is 4.5 for Bob and
11.7 for Jim. Which player should win the trophy for the most valuable player? Justify
your decision using standard deviation.
Mrs. Reeves returned the statistics test to her class. She offered students the opportunity
to gain one mark if they could explain the difference between their mark and their
percentile ranking. Pascal earned 83% and is in the 74th percentile. If Pascal wants to
earn the bonus mark, how would he explain the difference?
State the type of correlation that likely exists between the population of a city and the size
of its police force.
Toni scored 47 out of 60 on her exam. Five students received the same score as she did
but 20 received a lower score. If 34 students wrote the exam, calculate Toni’s percentile
A manufacturer produces tires. The number of trouble-free kilometres follow a normal
distribution and are shown in the graph below.
A) State the mean and standard deviation. (1 mark)
B) If 95 000 tires are manufactured how many tires are within one standard deviation
of the mean? (1 mark)
Determine the type of correlation that exists in the following table.
Nemo and Sponge Bob individually entered a science contest with 148 other students. They
each scored 91%. No one else scored the same as Nemo and Sponge Bob and 123 students
A) Calculate Nemo’s percentile rank. (1.5 marks)
B) The top 20% received a certificate of excellence and the top 10% received a medal.
What will Nemo receive? Justify your answer. (1 mark)
The results of a class test follow a normal distribution with a mean of 65 and a standard
deviation of 7.5.
A) What percentage of the students scored 50 or higher? (1 mark)
B) What is Chad’s score if he is told that 84% of the students scored lower than he did?
St. Herbert High School’s scores on a test were:
40, 60, 64, 64, 66, 66, 68, 68, 72, 92
A) Determine the mean score. (0.5 mark)
B) Determine the standard deviation on the test. (1.5 marks
Ramon received a test score that was in the 60th percentile. Three other people scored the
same as Ramon and 58 people scored lower. Determine the total number of people that
completed the test.
Fred and Barney are arguing over who performed better on the mathematics exam. Fred
received a mark of 70% and Barney scored in the 70th percentile. Barney believes he
performed better. In your opinion, who had the better result? Justify your answer.
Tammy wrote a statistics test in math class. The teacher found 2 errors in Tammy’s
calculation of percentile rank.
State the 2 errors Tammy made
The life expectancy of a Mipod battery follows a normal distribution. The mean life
expectancy of a Mipod battery is 18 months with a standard deviation of 3 months
A) Find the percent of Mipod batteries that will last between one and two years. (1 mark)
B) Explain, with reference to the normal curve, if it is possible to expect your Mipod battery to
work after 30 months. (1 mark)
Given the following graph:
B) State an appropriate r-value for this data. (0.5 mark)