Question
business analytics
According to a survey by consulting firm Watson Wyatt, approximately 19% of employers have eliminated perks or plan to do so in the next year (Kiplinger's Personal Finance, February 2009). Suppose 30 employers are randomly selected. a. What is the probability that exactly ten of the employers have eliminated or plan to eliminate perks? b. What is the probability that at least ten employers, but no more than 20 employers, have eliminated or plan to eliminate perks? c. What is the probability that at most eight employers have eliminated or plan to eliminate perks? According to the CGMA Economic Index, which measures executive sentiment across the world, 18% of all respondents expressed optimism about the global economy (www.aicpa.org, March 29, 2012). Moreover, 22% of the respondents from the United States and 9% from Asia felt optimistic about the global economy? a. What is the probability that an Asian respondent is not optimistic about the global economy? b. If 28% of all respondents are from the United States, what is the probability that a respondent is from the United States and is optimistic about the global economy? c. Suppose 22% of all respondents are from Asia. If a respondent feels optimistic about the global economy, what is the probability that the respondent is from Asia? Suppose you draw three cards, without replacement, from a deck of well shuffled cards. Remember that each deck consists of 52 cards, with 13 each of spades, hearts, clubs, and diamonds. a. What is the probability that you draw all spades? b. What is the probability that you draw two or fewer spades? c. What is the probability that you draw all spades or hearts?
Explanation / Answer
Solution:-
8)
p = 19/100
p = 0.19
a) The probability that exactly ten of the employers have eliminated or plan to eliminate perks is 0.027.
p = 0.19, n = 30, x = 10
By applying binomial distribution:-
P(x, n, p) = nCx*p x *(1 - p)(n - x)
P(x = 10) = 0.027
b) The probability that atleast ten employers, but no more than 20 employers have eliminated or plan to eliminate perks is 0.04507.
p = 0.19, n = 30
x1 = 10
x2 = 20
By applying binomial distribution:-
P(x, n, p) = nCx*p x *(1 - p)(n - x)
P(10 < x < 20) = P(x > 10) - P(x > 20)
P(10 < x < 20) = 0.04508 - 0.00001
P(10 < x < 20) = 0.04507
c) The probability that at most eight employers have eliminated or plan to eliminate perks is 0.89965.
p = 0.19, n = 30, x = 8
By applying binomial distribution:-
P(x, n, p) = nCx*p x *(1 - p)(n - x)
P(x < 8) = 0.89965
