Question

Homework 4: Probability and z scores

14. Use the data to answer the following questions
14. Show all work (*round 2 decimals places)

• What is the mean & SD for the distribution of scores?
• What is the corresponding z score for each raw score?
• What is the probability of getting a raw score greater than 4?
• What is the probability of getting a raw score less than 2?
• What is the probability of a raw score between 4 & 6?
• What is the probability of a raw score between 3 & 6?

Variable 2: # of traffic violations
2
5
5
3
2
1
1
6
2
4

Answer 1

The data points which is the number of traffic violations are

2, 5, 5, 3, 2, 1, 1, 6, 2, 4

1) mean is the average of the data points = (2+5+5+3+2+1+1+6+2+4)/10 = 3.1

The standard deviation formula is = 1.79

2) Z score of first raw point 2 is (2-mean)/SD = 2-3.1/1.79 = -0.615

Z score of 5 = (5-3.1)/1.79 =1.06

Z score of 1 = (1-3.1)/1.79 =-1.17

Z score of 6 = (6-3.1)/1.79 = 1.62

Z score 4 = (4-3.1)/1.79 =0.502

3) Probability of getting greater than 4 = number of times the data point is greater than equal to 4/total number of observations = 4/10 = 0.4

4) Probability of getting raw score less than 2 = number of times the data point is less than 2/total number of observations =2/10 = 0.2

5)Probability that the score is between 4 and 6= number of times the data point is less than 6 and greater than 5/total number of observations =2/10 = 0.2

6)Probability that the score is between 3 and 6= number of times the data point is less than 6 and greater than 3/total number of observations =3/10 = 0.3