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STAT-1770-B1-Intro. to Probability & Stat.
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In China, four-year-olds average three hours a day unsupervised. Most of the unsupervised children live in rural areas,considered safe. Suppose that the standard deviation is 1.5 hours and the amount of time spent alone is normally distributed. We randomly select one Chinese four-year-old living in a rural area. We are interested in the amount of time the child spends alone per day.
(a) In words, define the random variable X.
(b). X ~ _____(_____,_____)
(c) Find the probability that the child spends less than one hour per day unsupervised. Sketch the graph, and write the probability statement.
(d). What percent of the children spend over ten hours per day unsupervised?
(e). Seventy percent of the children spend at least how long per day unsupervised?
Your statistics instructor claims that 60 percent of the students who take her Elementary Statistics class go through lifefeeling more enriched. For some reason that she can't quite figure out, most people don't believe her. You decide to checkthis out on your own. You randomly survey 64 of her past Elementary Statistics students and find that 34 feel more enrichedas a result of her class. Use the steps discussed in class to perform an hypothesis test for this case. Include relevant graph sketch to indicate the rejection region. Now, what do you think?
A Newspaper advertisement read "The average man’s I.Q. is 107. The average brown trout’s I.Q. is 4. So why can’t man catch brown trout?" Suppose you believe that the brown trout’s mean I.Q. is greater than four. You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5; 4; 7; 3; 6; 4; 5; 3; 6; 3; 8; 5. Conduct a hypothesis test of your belief using the steps discussed in class. Ensure you add essential graph sketch to indicate the rejection region
According to a recent survey of 1,200 people, 61% feel that the presidentis doing an acceptable job. We are interested in the population proportionof people who feel the president is doing an acceptable job.(a) Define the random variables X and P in words.(b) Which distribution should you use for this problem? Explain yourchoice.(c) . Construct a 90% confidence interval for the population proportionof people who feel the president is doing an acceptable job.
(i) State the confidence interval.
(ii) Sketch the graph.
(iii)Calculate the error bound.
The Weather Underground reported that the mean amount of summerrainfall for the northeastern US is at least 11.52 inches. Ten cities in thenortheast are randomly selected and the mean rainfall amount is calculatedto be 7.42 inches with a standard deviation of 1.3 inches. At the α = 0:05level, can it be concluded that the mean rainfall was below the reportedaverage? What if α = 0:01 Assume the amount of summer rainfall follows a normal distribution.
The US Department of Energy reported that 51:7% of homes were heatedby natural gas. A random sample of 221 homes in Kentucky found that115 were heated by natural gas. Does the evidence support the claim forKentucky at the α = 0:05 level in Kentucky? Are the results applicable across the country? Why?
A pharmaceutical company makes tranquilizers. It is assumed that thedistribution for the length of time they last is approximately normal.Researchers in a hospital used the drug on a random sample of ninepatients. The effective period of the tranquilizer for each patient (inhours) was as follows: 2.7; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.(a) What is (i) ¯(x) (ii) Sx (iii) n (iv) n{1(b) Define the random variable X in words.(c) Define the random variable X¯ in words.(d) Which distribution should you use for this problem? Explain yourchoice.(e) Construct a 95% confidence interval for the population mean lengthof time. (i) State the confidence interval. (ii). Sketch the graph. (iii).Calculate the error bound.(f) What does it mean to be "95% confident" in this problem?
The switchboard in a Minneapolis law office gets an average of 5.5incoming phone calls during the noon hour on Mondays. Experience showsthat the existing staff can handle up to six calls in an hour. Let X = thenumber of calls received at noon.(a) Find the mean and standard deviation of X.(b) What is the probability that the office receives at most six calls atnoon on Monday?(c) Find the probability that the law office receives six calls at noon.What does this mean to the law office staff who get, on average, 5.5incoming phone calls at noon?(d) What is the probability that the office receives more than eight calls at noon?
A student takes a 32-question multiple-choice exam, but did not study andrandomly guesses each answer. Each question has three possible choicesfor the answer. Find the probability that the student guesses more than 75% of the questions correctly?