Determine whether or not each of the following experiments represents a binomial

Question

Determine whether or not each of the following experiments represents a binomialexperiment.

a. A die is rolled 20 times and the number of 6’s is counted.b. A die is rolled until ten 6’s show up.c. In a stream with 1,500 fish, 700 are Rainbow Trout. A total of 20 fish are caughtand the number of Rainbow Trout is counted.d. About 10% of the U.S. population is suspected to have a form of bacteria. Asample of 100 people is drawn from the population and the number of people withthe strain of bacteria is counted.e. A brand of LED light bulb has a 0.5% chance of going out prior to the advertisedlife of 30,000 hours. In the testing phase, 850 bulbs are sampled for quality
assurance. The number of bulbs that don’t die prior to the 30,000 hour life is

counted.

Explanation / Answer

Solution:-

a) A die is rolled 20 times and the number of 6’s is counted.

This experiments represents a binomial experiment.

n = 20, p = 0.1667, x = number of 6.

b) A die is rolled until ten 6’s show up.

This experiments does not represents a binomial experiment, becuase the number of trials are not fixed.

c) In a stream with 1,500 fish, 700 are Rainbow Trout. A total of 20 fish are caughtand the number of Rainbow Trout is counted.

This experiments represents a binomial experiment.

n = 20, p = 700/1500 = 0.467, x = number of Rainbow Trout is counted.

d.) About 10% of the U.S. population is suspected to have a form of bacteria. A sample of 100 people is drawn from the population and the number of people with the strain of bacteria is counted.

This experiments represents a binomial experiment.

p = 0.10, n = 100, x = number of people with the strain of bacteria is counted.

e.) A brand of LED light bulb has a 0.5% chance of going out prior to the advertisedlife of 30,000 hours. In the testing phase, 850 bulbs are sampled for quality assurance. The number of bulbs that don’t die prior to the 30,000 hour life is counted.

This experiments represents a binomial experiment.

p = 0.005, (1 - p) = 0.995, n = 850, x = number of bulbs that don’t die prior to the 30,000 hour life is counted

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