Question

It is known that 80% of all brand a zip drives work in a sat isfactory manner throughout the warranty period (are ‚äúsuc cesses‚äù). suppose that n 10 drives are randomly selected. let x the number of successes in the sample. the statis tic x/n is the sample proportion (fraction) of successes. obtain the sampling distribution of this statistic. [hint: one possible value of x/n is .3, corresponding to x 3. what is the probability of this value (what kind of random variable is x)?]

Answer 1

The sampling distribution of the sample proportion of successes in randomly selected zip drives can be approximated by a normal distribution when certain conditions are met. The random variable representing the number of successes follows a binomial distribution, and the probability of a specific value can be calculated using the binomial probability formula.

Step-by-step explanation:

The sampling distribution of the statistic x/n, which represents the sample proportion of successes, can be approximated by a normal distribution when certain conditions are met. The conditions include having a certain number of independent trials (n), each trial having the same probability of success (p), and both np and n(1-p) being greater than five. In this case, the random variable x follows a binomial distribution, and the probability of a specific value, such as x=3, can be calculated.

The random variable x follows a binomial distribution because it represents the number of successes in the sample, and each trial (selecting a zip drive) can either be a success (work satisfactorily) or a failure (not work satisfactorily). The probability of x=3 can be calculated using the binomial probability formula: P(X=3) = (nC3)p^3(1-p)^(n-3), where n is the sample size and p is the probability of success (0.8).