IV. In a job fair, 3000 applicants applied for a job, their mean age
was found to be 28 with standard deviation for 4 years.
a. Draw a normal curve distribution showing the z-score and the raw
scores.
b. How many applicants are above 32 years old?
c. How many have ages between 24 and 32 years?

To draw the normal curve distribution, you start by plotting the mean age of 28. Since the standard deviation is 4 years, you can calculate the z-scores for different ages. For example, an age of 32 has a z-score of (32-28)/4 = 1. Similarly, for age 24, the z-score is (24-28)/4 = -1. The curve will peak at 28, with points around 24 and 32 forming the bell shape.

To find the number of applicants above 32 years old, first calculate the z-score for 32: z = (32-28)/4 = 1. Looking at the z-table, a z-score of 1 corresponds to about 84.13%. This means approximately 15.87% of applicants, or about 476 people (0.1587 * 3000), are older than 32 years.

For ages between 24 and 32, you would use the z-scores of -1 and 1. The area between these z-scores covers approximately 68.27% of the data. Thus, around 2,048 applicants (0.6827 * 3000) fall within this age range.