Question
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?
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?
Ask by Wood Warner. in the Philippines
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
- a. The normal distribution curve shows key ages at z-scores of -2 (20 years), -1 (24 years), 0 (28 years), +1 (32 years), and +2 (36 years).
- b. Approximately 476 applicants are above 32 years old.
- c. About 2,048 applicants are between 24 and 32 years old.
Solution
Sure, let’s tackle each part of the problem step by step.
Given:
- Total applicants: 3,000
- Mean age (
): 28 years - Standard deviation (
): 4 years
a. Drawing the Normal Distribution Curve
While I can’t provide a visual graph here, I can describe how to sketch the normal distribution curve with the relevant z-scores and raw scores:
-
Draw the Bell Curve: Start with the classic symmetric bell-shaped curve representing the normal distribution.
-
Mark the Mean:
- Center Point: Plot a vertical line at the mean age,
years.
- Center Point: Plot a vertical line at the mean age,
-
Identify Key Points Using Z-Scores:
- Z-score Formula:
- Common Z-scores:
-
corresponds to years -
corresponds to years -
(the mean) corresponds to years -
corresponds to years -
corresponds to years
-
- Z-score Formula:
-
Label the Curve:
- Place vertical lines at 20, 24, 28, 32, and 36 years.
- Label each line with its corresponding z-score (-2, -1, 0, +1, +2).
Summary of Key Points on the Curve:
| Z-score | Age (X) |
|---|---|
| -2 | 20 |
| -1 | 24 |
| 0 | 28 |
| +1 | 32 |
| +2 | 36 |
b. Number of Applicants Above 32 Years Old
-
Calculate the Z-score for 32 years:
-
Find the Probability § for
: - Using the standard normal distribution table,
(15.87%).
- Using the standard normal distribution table,
-
Calculate the Number of Applicants:
Answer: Approximately 476 applicants are above 32 years old.
c. Number of Applicants Between 24 and 32 Years Old
-
Calculate the Z-scores for 24 and 32 years:
- For 24 years:
- For 32 years:
- For 24 years:
-
Find the Probability § for
: - Using the standard normal distribution table,
(68.26%).
- Using the standard normal distribution table,
-
Calculate the Number of Applicants:
Answer: Approximately 2,048 applicants have ages between 24 and 32 years.
Summary of Answers
- a. Described the normal distribution curve with key z-scores and raw scores.
- b. ~476 applicants are above 32 years old.
- c. ~2,048 applicants have ages between 24 and 32 years.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Explain 
Simplify this solution The Deep Dive
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.
