Question

In SUMMER 2018 session, Sonia Buchanan, took four final exams. The exam mean and standarddeviation for each course (class) along with Sonia’s score on each exam are listed in table below.Assume that the grades on each exam are NORMALLY DISTRIBUTED.

Exam	Mean for cohort (class)	Standard deviation for cohort (class)	Daniel’s score
Introduction to Sociology Life and Teachings of Christ Principles of Psychology Freshman Composition II	75 85.6 83 70.4	4.2 6.7 4.9 6.4	79 91 88 76

1. Discuss the importance of the normal distribution curve in the Behavioural Sciences

2. With respect to the normal curve what is a percentile rank? Give an example using a diagram

3. Calculate Sonia's percentile rank for the Life and Teachings of Christ

4. On which exam did Sonia do best relative to the other students in the class

Answer 1

1. Common patterns of numbers includes most of the measurements being clustered together near the mean of the distribution, with few cases occurring as they deviate away from the mean. When a frequency distribution is drawn in pictorial form, the resulting pattern produces the bell-shaped curve that scientists call a normal distribution

For the measurement of behavior, normal distribution helps us in following ways

- For the normal distributions the measurement results in numbers that differ from one another individually but that are predictable as a group (better for analysis and decision making)

- Normal distribution can help us in the possibility of determination of the behaviors that will occur and the proportion of them which are less likely to occur

2. The percentile rank of a score is the percentage of scores in normal distribution that are equal to or lower than it. For example, a test score that is > than 65% of the scores of people taking the test is said to be at the 65th percentile, where 65 is the percentile rank

3.

Using Z-score, we can look up the z-distribution table (available in every stats book/google) we can find the percentile, in this case it is 78.9th percentile

Posting graph using minitab

4. To find out best subject - doing same exercise for all subjects

Exam	Mean for cohort (class)	Standard deviation for cohort (class)	Daniel’s score		z-value		Percentile
Introduction to Sociology	75	4.2	79		0.952381		82.9
Life and Teachings of Christ	85.6	6.7	91		0.80597		78.9
Principles of Psychology	83	4.9	88		1.020408		84.6
Freshman Composition II	70.4	6.4	76		0.875		80.9

The best performing subject is Principles of Psychology