Questions 18-21 are based on the following information: 18. Human Resources Depa

Question

Questions 18-21 are based on the following information: 18. Human Resources Department of onc hotel reports th Human Resources Department of one hotel reports that annual salaries for its personnel have a mean of $40,000 and a standard deviation of $3,500. If the sala ries are symmetrically distributed, the interval of salaries representing two standard deviations on either side of the mean is A. (33000, 47000) B. (36500, 43500) C. (29500, 55000) D. (42000, 53000) 19. What proportion of the salaries is within $3,500 of the mean? A. 95% B. 99% C. 84% D. 68% 20. What proportion of the salary is below $33,000? A. 5% B. 2.5% C. 10% D.190

Explanation / Answer

Ans:

18)95% of the data falls within 2 standard deviations of the mean

so,

lower limit=40000-2*3500=33000

upper limit=40000+2*3500=47000

Option A is correct (33000, 47000)

19)68% of the data falls within one standard dveiation of the mean

Option D is correct(68%)

20)33000 is 2 standard deviations below mean

95% data falls within 2 standard deviations and 5% falls outside,so half of 5% i.e. 2.5% falls below 2 standard deviation.

Option B is correct(2.5%)

21)when not symmetrical,use chebyshev's theorm

k=5/2=2.5

Proportion of salaries that are 2,5 standard deviation of the mean=1-(1/k^2)

=1-(1/2.5^2)

=0.84 or 84%

Option D is correct(84%)

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