Question

speed (mph) 16.27 16.57 16.7 17.17 17.84 18.5 18.59 18.71 18.88 19.11 19.64 20.1 20.2 20.28...

speed (mph)

16.27

16.57

16.7

17.17

17.84

18.5

18.59

18.71

18.88

19.11

19.64

20.1

20.2

20.28

20.62

20.64

20.65

20.73

20.76

20.82

21.17

21.22

21.23

21.53

21.54

21.57

21.6

21.75

21.78

21.79

21.89

21.91

21.97

21.97

22.33

22.35

22.41

22.47

22.58

22.73

22.96

23.04

23.07

23.11

23.25

23.43

23.45

23.46

23.5

23.52

23.53

23.54

23.59

23.75

23.86

24.02

24.07

24.12

24.18

24.19

24.23

24.26

24.3

24.56

24.76

25.19

25.21

25.3

25.45

25.49

25.52

25.6

25.7

25.7

25.71

25.81

26.07

26.09

26.33

26.65

27.28

27.34

27.49

27.61

27.87

28.06

28.28

28.45

28.81

28.96

28.98

29.51

29.53

29.94

29.97

30.03

30.1

30.72

31.26

34.06

1. calculate the five number summary, the mean, and standard deviation of the 100 readings.

2. Do you believe a Normal model is appropriate for this data set? Refer to your normal probability plot and consider the mean and median from Number 1 to help you explain this.  

3. Find the number of cars that were speeding (that is, the number of cars traveling over 20 mph), by typing the command length(x[x>20]) where x is your data. What is this as a proportion of the whole data set?

4. Since this data is representative it seems reasonable to use a normal model for the speed of all the vehicles that pass by this house. Using the mean and standard deviation for a normal model of the car speeds (from Number 1), calculate the proportion of vehicles that should be speeding according to the normal model, that is, P(x>20), where x is a vehicle’s speed. How does this compare to your answer in Number 3? Are they close?

5. Using the mean and standard deviation for a normal model of the car speeds (from Number 1), calculate the proportion of vehicles that should be speeding according to the normal model, that is, P(x>20), where x is a vehicle’s speed. How does this compare to your answer in Number 4? Are they close?

6. Using your normal model from Number 5, what proportion of all vehicles have speeds under 20 mph?

7. Using your normal model from Number 5, what speed marks off the top 5% of fastest vehicles?  

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

1.

Variable Mean StDev Minimum Q1 Median Q3 Maximum
speed (mph) 23.844 3.563 16.270 21.547 23.525 25.785 34.060

2.

From normal probability plot and since mean is almost same as median so we believe that Normal model is appropriate for this data set.

3. The number of cars traveling over 20 mph=89

4.

6.

6.

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