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An oil prospector will drill a succession of holes in a given area to find a productive well. The probability that he is successful on a given trial is .2.
(a) What is the probability that the third hole drilled is the first to yield a productive well?
(b) If the prospector can afford to drill at most ten wells, what is the probability that he will fail to find a productive well?
Ten motors are packaged for sale in a certain warehouse. The motors sell for $100 each, but a double-your-money-back guarantee is in effect for any defectives the purchaser may receive. Find the expected net gain for the seller if the probability of any one motor being defective is .08. (Assume that the quality of any one motor is independent of that of the others.)
A missile protection system consists of n radar sets operating independently, each with a probability of .9 of detecting a missile entering a zone that is covered by all of the units.
(a) If n = 5 and a missile enters the zone, what is the probability that exactly four sets detect the missile? At least one set?
(b) How large must n be if we require that the probability of detecting a missile that enters the zone be .999?
A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has four identical components, each with a probability of .2 of failing in less than 1000 hours. The subsystem will operate if any two of the four components are operating. Assume that the components operate independently. Find the probability that;
(a) Exactly two of the four components last longer than 1000 hours.
(b) The subsystem operates longer than 1000 hours.
A multiple-choice examination has 15 questions, each with five possible answers, only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess. What is the probability that he answers at least ten questions correctly?
On the Standford-Binet test, the mean IQ is 100. A class of 21 kindergarten pupils were tested with a resulting mean of 105 and a standard deviation of 5.44. Does this group have a mean significantly different than the norm group? Use 0.01 as your level of significance.
A random sample of 11 cigarettes of a certain brand has an average nicotine content of 6.6 milligrams and a standard deviation of 2.5 milligrams. Is this in line with the manufacturer's claim that the average nicotine content does not exceed 4.2 milligrams? Use 0.1 level of significance.
According to Dietary Goals for the US (1977), high sodium intake may be related to ulcers, stomach cancer, and migrane headaches. The human requirement for salt is less than 220 milligrams per day, which is surpassed in most single servings of ready-to-eat noodles. If a random sample of 22 similar servings of noodles has a mean sodium content of 210 milligrams and a standard deviation of 5.23 does this suggest at the 0.01 level of significance that the average sodium content for a single servings of noodles is less than 220 milligrams?
b. How long will a call be responded if it has a z-score of – 1.83?
A random variable has PDF p_i = 2(1/3)^i and takes on values in the positive integers. What is the probability that it takes on a value between 10 and 20, inclusive? Show your work step by step.
