A box contains four 40-W bulbs, five 60-W bulbs and six 75-W bulbs. Bulbs are se

Question

A box contains four 40-W bulbs, five 60-W bulbs and six 75-W bulbs. Bulbs are selected randomly and without replacement. To two decimal point accuracy, the probability that at least two bulbs must be selected to obtain one that is rated 75 W is: a. 0.70. b. 0.89. c. 0.93. d) 0.60. e. none of the above. If a population proportion p is unknown, the number of subjects that would need to be sampled such that a 95 percent confidence interval for p has an interval width of at most two percentage points is: a. 193. b. 1068. c. 9604. d. 38416. e. none of the above.

Explanation / Answer

problem 7)

Box contains four 40-W bulbs,five 60-W bulbs, six 75-W bulbs

total no of bulbs = 4+5+6 = 15

probabilty that first bulb selected is of 75-W = 6/15 = 0.4

probability that at least two bulbs must be selected to obtain one that is rated 75-W = probabilty that first bulb selected is not of 75-W = 1- probabilty that first bulb selected is of 75-W = 1- 0.4 = 0.6

5)

let n be the number of subjects that need to be sampled

standard deviation of p = [p*(1-p)/n]0.5

interval width of p = 2*1.96*(standard deviation of p)

maximum value for standard deviation of i.e for p=0.5 =  [0.5*(1-0.5)/n]0.5 = [0.25/n]0.5

maximum interval width of p =  2*1.96*[0.25/n]0.5

but given that max interval width is 2% or 0.02

2*1.96*[0.25/n]0.5 = 0.02 => (0.25/n) = (0.01/1.96)2 =0.00002603082

0.25/n = 0.00002603082

n = 0.25/0.00002603082 = 9604

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