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- A new battery's voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found. Suppose that 91% of all batteries have acceptable voltages. Let Y denote the number of batteries that must be tested. (a) What is p(2), that is P(Y= 2)? (Round your answer to four decimal places.) p(2) = (b) What is p(3)? [Hint: There are two different outcomes that result in Y = 3.]. (Round your answer to three decimal places.) p(3) = (c) To have Y = 5, what must be true of the fifth battery selected? O The fifth battery must be an A. O The fifth battery must be a U. List the four outcomes for which Y = 5. (Enter your answer in set notation.) Determine p(5). (Round your answer to five decimal places.) p(5) = (d) Use the pattern in your answers for parts (a)-(c) to obtain a general formula for p(y). p(y) =Consider sample data with x = 10 and s = 2. (a) Compute the coefficient of variation (in percent). % (b) Compute a 75% Chebyshev interval around the sample mean. (Enter your answer in the form: lower limit to upper limit. Include the word "to.")Is (∑i=2 Xi)/(n-1) a consistent and unbiased estimator of E(X)? Explain your result.
- a11 (a) Discuss the two expressions -x;- )² and E(x;- )², both of which are used (n-1) i=1 to measure the spread of a set of observations x1, x2, . .., X. (b) A random sample of n observations is taken from a distribution; the sum of the observations is t, and the sum of the squares of the observations is 12. Explain how to estimate the mean and the variance of the distribution from which the random sample was taken. (c) Given the random sample described in part (b), write down expressions (based on 11 and t2) for estimates of the mean and variance of the mean of a further, independent, random sample of size m , from the original distribution. (d) Given that n = 25, 1, = 400 and t2 = 8800, construct a 99% confidence interval for the mean of the distribution, and use it to test whether or not this mean could be 20.Please solve within 20 minutes