Statistics with TI-Nspire™ Technology

Module E

Lesson 3: Exercises

Statistics with TI-Nspire™ Technology

Module E

In the previous lesson you learned:

How to generate a random sample. To calculate statistics of a sample. To draw a histogram and change the bin settings. To draw a function above the histogram and compare the histogram with

the distribution of the population. To draw a box-plot and a dot-plot. To use the dynamic link between the plots and the data to explain the

difference between the mean and the median.

3 | Lesson E.3

In this lesson you will:

• Use the TI-Nspire software, installed on your computer to do some exercises.

• Examine the relationship between the speed of a car and its stopping distance.

• Check a statement about probability density functions.• Practice the things you learned in the previous lessons.

4 | Lesson E.3

TI-Nspire™ Technology

Exercise 1

• Many drivers drive in a false belief that if the car in front suddenly starts braking, they would react and brake and end up stopped the same distance apart.• The total stopping distance of a vehicle is made up of 2 components:

• Human Reaction Time (reaction distance)• Vehicle Braking Capability (braking distance)

• The human reaction time is how long the body takes to move the foot from accelerator to the brake pedal. This reaction time can vary from ¼ - ¾ of a second. This is a human factor and as such can be affected by tiredness, alcohol and concentration levels. • The vehicle braking capability determines how long it takes to stop the car, once the brake pedal is pushed.

5 | Lesson E.3

Exercise 1

• For several speeds you can see the reaction distance and the braking distance of a car in good weather conditions.

Speed(km/h)

Reaction distance(m)

Braking distance(m)

30 9 5

50 14 13

70 19 25

90 25 41

120 33 72

140 39 98

• Question: Examine the relationship between the reaction distance and the speed, and between the braking distance and the speed.

6 | Lesson E.3

Exercise 2

• The larger the sample the better the sample distribution looks like the distribution of the population.

QUESTION:

Use TI-Nspire Technology to illustrate this statement for a normal population of lengths of 17 years old boys with mean 178 cm and standard deviation 7 cm. Use a sample of 10, 100, 500 and 1000 values.

7 | Lesson E.3

Congratulations!

You have just finished lesson E.3!

8 | Lesson E.3