According to a report from a business intelligence company, smartphone owners are using an average of 19 apps per month. Assume that number of apps used per month by smartphone owners is normally distributed and that the standard deviation is 5. Complete parts (a) through (d) below. a. If you select a random sample of 36 smartphone owners, what is the probability that the sample mean is between 18.5 and 19.5? 0.452 (Round to three decimal places as needed.) b. If you select a random sample of 36 smartphone owners, what is the probability that the sample mean is between 18 and 19? 0.385 (Round to three decimal places as needed.) c. If you select a random sample of 144 smartphone owners, what is the probability that the sample mean is between 18.5 and 19.5? 0.770 (Round to three decimal places as needed.) d. Explain the difference in the results of (a) and (c). The sample size in (c) is greater than the sample size in (a), so the standard error of the mean (or the standard deviation of the sampling distribution) in (c) is greater than in (a). As the standard error increases, values become more concentrated around the mean. Therefore, the probability that the sample mean will fall close to the population mean will always decrease when the sample size increases.Apoiitical pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a twcrcandidate election' ifa specic candidate receives at least 55% of the vote in the sample, that candidate will be forecast as the winner of the election. You select a random sample of 100 voters. Complete parts (a) through (c) below a. What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 50.1 91:? The probability is 0.1635 that a candidate will be forecast as the winner when the population percentage of her vote is 50.1 91:. (Round to four decimal places as needed.) b. What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 59%i The probability is 0.?920 that a candidate will be forecast as the winner when the population percentage of her vote is 59%. (Round to four decimal places as needed.) c. What is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 49% {and she will actually lose the election)? The probability is that a candidate will be forecast as the winner when the population percentage of her vote is 49%. (Round to four decimal places as needed.) A marketing survey is conducted in which students are to taste two different brands of soft drink. Their task is to correctly identify the brand tasted. A random sample of 180 students is taken. Assume that the students have no ability to distinguish between the two brands. Complete (a) through (d) below. a. What is the probability that the sample will have between 50% and 55% of the identifications correct? 0.4101 (Round to four decimal places as needed.) b. The probability is 90% that the sample percentage is contained within what symmetrical limits of the population percentage? Identify the limits of the population percentage. The lower limit is 0.4387. The upper limit is 0.5613 . (Round to four decimal places as needed.) There is a 90% probability that the sample percentage will be contained within 12.3 % symmetrically around the population percentage. (Round to the one decimal place as needed.)