The mean income for a sample of 75 part-time assistants at IIUM is RM800 and the standard deviation is RM40.
a. According to Chebyshev’s theorem, at least what percent of the income will lie between RM600 and RM1000?
b. How many of the part-time assistants will receive the income between RM600 and RM1000?
Guide On Rating System
Vote
a. According to Chebyshev's theorem, at least 75% of the data will lie within 2 standard deviations of the mean. Since the standard deviation is RM40, 2 standard deviations will be 2 * RM40 = RM80.
To find the range of income that lies between RM600 and RM1000, we need to determine how many standard deviations this range is from the mean.
For RM600:
(Z-score) = (X - Mean) / Standard Deviation
(Z-score) = (600 - 800) / 40
(Z-score) = -200 / 40
(Z-score) = -5
For RM1000:
(Z-score) = (X - Mean) / Standard Deviation
(Z-score) = (1000 - 800) / 40
(Z-score) = 200 / 40
(Z-score) = 5
Thus, the range of income from RM600 to RM1000 is equivalent to 5 standard deviations below the mean to 5 standard deviations above the mean.
According to Chebyshev's theorem, at least 75% of the income will lie within this range.
b. To find the number of part-time assistants that will receive income between RM600 and RM1000, we need to determine the proportion of the sample that lies within this range.
According to Chebyshev's theorem, at least 75% of the data lies within 2 standard deviations of the mean. This means that the proportion of the sample that lies outside this range is (100 - 75)% = 25%.
Since we have a sample size of 75, the number of part-time assistants that will receive income between RM600 and RM1000 is 75 * (1 - 0.25) = 75 * 0.75 = 56.25 or approximately 56.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99