Question

ON EXCEL.

22, 2012), Suppose that a random sample of fifteen IS. to 34-year- olds living with their parents is selected and asked if they contribute to househo expenses. a. Is the selection of the fifteen 18- to 34-year-olds living with their parents a binomial experiment? Explain. If the sample shows that none of the fifteen 18- to 34-year-olds living with their parents contribute to household expenses, would you question the results of the Pew Research Study? Explain. What is the probability that at least 10 of the fifteen 18- to 34-year-olds living with their parents contribute to household expenses? b. c.

Answer 1

a) Yes, it is binomial experiment because 18-34 years olds are selected randomly and indepenednt of each other, and the probability of selecting the samples are constant from trial to trial. , and there are only two outcomes , i.e. contribute to household expenses and do not contribute to household expenses.

b)

The Probability that none of the fifteen 18 -34 year olds living with their parents contribute to household expenses is

$P(X=0) = \binom{15}{0}(0.5)^{0}(0.5)^{15-0} =(0.5)^{15} = 0.00003052$

Since the probability is very low , we would ask about the results of the Pew Research Study, to check, whether there is any baisedness in collecting data .

c)  

$P(X\geq 10) = P(X=10)+P(X=11)+.....+P(X=15)$

$P(X = 10) = \binom{15}{10}(0.5)^{10}(0.5)^{15-10} =0.0916$

$P(X = 11) = \binom{15}{11}(0.5)^{11}(0.5)^{15-11} =0.0417$

$P(X = 12) = \binom{15}{12}(0.5)^{12}(0.5)^{15-12} =0.1386$

$P(X = 13) = \binom{15}{13}(0.5)^{13}(0.5)^{15-13} =0.0032$

$P(X = 14) = \binom{15}{14}(0.5)^{14}(0.5)^{15-14} =0.00046$

$P(X = 15) = \binom{15}{15}(0.5)^{15}(0.5)^{15-15} =0.00003052$

$P(X\geq 10) = P(X=10)+P(X=11)+.....+P(X=15) =0.1509$