Unit 3 Statistics Exam

Question 1

(2 marks) Show your work and draw box(es) around your final answer(s).

The data below show the results of a pop quiz.

75 41 63 81 46 38 96 91 56 75 74 100 46 75 56 77

Determine the following, rounded to the nearest tenth when necessary.

a. What was the mean score?

b. What was the mode?

Question 2

(2 marks) Show your work and draw box(es) around your final answer(s).

The following were the exam scores for the last math quiz.

Determine the following, rounded to the nearest tenth when necessary.

a. What was the median score?

b. What was the standard deviation?

Question 3

(2 marks) Show your work and draw box(es) around your final answer(s). Include a therefore statement.

Everly requires an 80% average for her four prerequisite courses to get into her career program. She currently has the following marks in three of those courses:

• Nursing Math - 73%
• Anatomy - 82%
• Communications - 91%

If all courses carry the same weight, what mark will she need in her fourth course, Drug Administration?

Question 4

(1 mark) Circle the correct answer.

The lifetimes of HotNStepped kettles are normally distributed with a mean of 38 months and a standard deviation of 8 months.

If a chain of stores sells 2800 of these kettles and gives an 18 month warranty, how many of them would be expected to fail before the warranty expires?

a. 8

b. 17

c. 83

d. 170

Question 5

(3 marks) Show your work and draw box(es) around your final answer(s). Include a therefore statement.

During the past many summers, Ross and Rachel have had tourists stay at their bed and breakfast. On average they receive 420 tourists and during the last summer, with a standard deviation of 15 tourists and a z-score for the last summer of business of -0.87.

a. How do you know that the last summer of business was not as good as usual?

b. How many tourists did they receive last summer?

Question 6

(1 mark) Circle the correct answer.

Annabell recently took four different exams in four different courses. She found out the class results and her own results. On which test did the student perform better, relative to the rest of the class?(Hint: Complete the z-score column.)

a. Mathematics

b. Biology

c. Basket Weaving

d. Bird Watching

Question 7

(4 marks) Show your work and draw box(es) around your final answer(s). Include therefore statements.

Richard owns his own business, delivering goods to people and businesses. On average, he drives 600 km per week, with a standard deviation of 50 km.

a. Sketch and label a normal distribution curve that represents this scenario.

b. What is the probability that he will drive between 650 and 800 km in a given week? Round your answer to the nearest hundredth.

c. What is the probability that he will drive less than 500 km in a given week? Round your answer to the nearest hundredth.

d. If the z-score for Richard's driving distance during a given week is 1.33, how many kilometres did he drive that week? Round your answer to the nearest whole kilometre.

Question 8

(2 marks) Show your work and draw box(es) around your final answer(s).

A poll of 1200 people showed that 43% of people will vote for Haley for Mayor of Airdrie. The margin of error of the study is 3.5%, 19 times out of 20.

a. What is the confidence level of this poll?

b. What is the confidence interval of the poll?

Question 9 (3 marks) Show your work and draw box(es) around your final answer(s). Include a therefore statement.

A hardware manufacturer produces bolts that have an average length of 1.23 in., with a standard deviation of 0.02 in. To be sold, all bolts must have a length between 1.21 in. and 1.26 in. What percent, to the nearest whole number, of the total production can be sold?