Assume the random variable x is normally distributed with mean p = 35 and standard deviation or: 5. Find the indicated probability. P(x {75} P(x 4: 7'5} = Cl (Round to four decimal places as needed.) The monthly utility bills in a city are normally distributed, with a mean of 100 and a standard deViation of $16. Find the probability that a randomly selected utility bill is (a) less than $66, (b) between $88 and $100, and (c) more than $130. alThe probability that a randomly selected utility bill is less than $66 is Round to four deCimal places as needed ) b)The probability that a randomly selected utility bill is between $58 and $100 is Round to four deCimal places as needed ) c) The probability that a randomly selected utility bill is more than $130 lS Round to four deCimal places as needed ) A population has a mean u = 87 and a standard deviation o = 12. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 36. H- = (Simplify your answer.) Of = (Simplify your answer.)The weights of ice cream cartons are normally distributed with a mean weight of 10 ounces and a standard deviation of 0.5 ounce. (a) What is the probability that a randomly selected carton has a weight greater than 10.18 ounces? (b}A sample of 36 cartons is randomly selected. What is the probability that their mean weight is greater than 10.18 ounces? (a}The probability is . (Round to four decimal places as needed.) (b}The probability is (Round to four decimal places as needed.) Find the margin of error for the given values of c, o, and n. c = 0.95, o = 2.6, n =64 Click the icon to view a table of common critical values. X Table of Common Critical Values E=(Round to three decimal places as needed.) Level of Confidence 90% 1.645 95% 1.96 99% 2.575 Print DoneConstruct the confidence interval for the population mean p. C = 0.98, x = 15.2, 6=9.0, and n = 100 A 98% confidence interval for u is (Round to one decimal place as needed.)Find the minimum sample size n needed to estimate u for the given values of c, o, and E. c = 0.95, o =6.3, and E = 2 Assume that a preliminary sample has at least 30 members. n = (Round up to the nearest whole number.)Let p be the population proportion for the following condition. Find the point estimates for p and 4:]. Of 304 children surveyed, 92 plan to join the armed forces in the future. The point estimate for p, E is D (Round to three decimal places as needed.) The point estimate for q, a is D (Round to three decimal places as needed.) In a survey of 2378 adults in a recent year, 1452 say they have made a New Year's resolution. Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. The 90% confidence interval for the population proportion p is (]) (Round to three decimal places as needed.) The 95% confidence interval for the population proportion p is (]]) (Round to three decimal places as needed.) With the given confidence, it can be said that the of adults who say they have made a New Year's resolution is of the given confidence interval. Compare the widths of the confidence intervals. Choose the correct answer below. O A. The 90% confidence interval is wider. O B. The 95% confidence interval is wider. O C. The confidence intervals are the same width. O D. The confidence intervals cannot be compared