Quiz 7: Binomial Distributions (Ch 6.2)
According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze. (a) What is the probability that among 16 randomly observed individuals exactly 6 do not cover their mouth when sneezing? (b) What is the probability that among 16 randomly observed individuals fewer than 4 do not cover their mouth when sneezing? (c) Would you be surprised if, after observing 16 individuals, fewer than half covered their mouth when sneezing? Why?
(a) The probability that exactly 6 individuals do not cover their mouth is 0.1299. (b) The probability that fewer than 4 individuals do not cover their mouth is 0.3460. (c) Fewer than half of 16 individuals covering their mouth would be surprising because the probability of observing fewer than half covering their mouth when sneezing is 0.0118, which is an unusual event.
Suppose that a recent poll found that 55% of adults believe that the overall state of moral values is poor. Complete parts (a) through (c). (a) For 300 randomly selected adults, compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor. (b) Interpret the mean. Choose the correct answer below. (c) Would it be unusual if 165 of the 300 adults surveyed believe that the overall state of moral values is poor?
A. The mean of X is 165. The standard deviation of X is 8.6. B. For every 300 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor. C. No.
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n=50, p=0.98, x=48
P(48)=0.1858
Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. A tennis player who aces 10% of her serves is asked to hit serves until she gets an ace. The number of serves attempted is recorded. Does the probability experiment represent a binomial experiment?
No, because the experiment is not performed a fixed number of times.