Question

you did not know that the aistributioh Was bell-shapea 8) Hope got a 76 on her last test in Psychology. The mean grade was an 82 and the standard deviation was 4 grade points. When she challenged her friend to a computer game, she scored a 4300. The mean score is a 4750 with a standard deviation of 400 points. Did Hope do relatively better on her test or her game? What measurement did you use? What information does this measurement give us? Where did we see it again later in the course? Anna had a z-score of -1.7 on the test and a z-score of 2.1 on the game. What was her grade and her game score? How do you know if a value is unusual? Which population is more variable? What measurement did you use? What is the value of this measurement for each of the two populations? DJCasey Maths 243 page 2 of 6
Please do #8 and explain each step in simple terms so I can understand how to do it. Thank you!

Answer 1

For all the questions mentioned above we'll use Z-score as the evaluator.
What is Z-score?
A z-score (standard score) indicates how many standard deviations an element is from the mean. A z-score can be calculated from the following formula. z = (X - μ) / σ where z is the z-score, X is the value of the element, μ is the population mean, and σ is the standard deviation.
The higher(+ve) Z-score indicates that the value is further above the Mean.
The lower(-ve) Z-score indicates that the value is further lower than the Mean.

1) Calculating Z score for test
   X= 76
   μ=82   σ=4
   Z score test = (76-82)/4 = -1.5
Calculating Z score for computer game
   X= 4300
   μ=4750   σ=400
   Z score test = (4300-4750)/400 = -1.125
As Z score for computer game > Z score of test, Hope performed better in computer game
2) We used z score as described above
3) The higher(+ve) Z-score indicates that the value is further above the Mean
The lower(-ve) Z-score indicates that the value is further lower than the Mean.
5) a)A z score of -1.7 indicates the performance was below average in the test
   z = (X - μ) / σ    z= -1.7   μ=82   σ=4
   X = σ *z + μ
   X= 75.2
b) A z score of 2.1 means the performance in game was above average
   z = (X - μ) / σ    z=2.1   μ=4750   σ=400
   X = σ *z + μ
   X = 5590
6) A value will be unusual if the z score is too high or too low or in other words it lies very away from the mean
7)The variability is measured on the basis of standard deviation
Population 1 (test) has a standard deviation of 4
Population 2 (game) has a standard deviation of 400
As the scales are different we need to normalize the values
So we calculate coefficient of variation = σ/μ
Population 1 = 4/82 = 0.048
Population 2 = 400/4750 = 0.084
Hence, Population 2 is more variable