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# DURING THE LAST WEEK OF THE SEMESTER, STUDENTS AT A CERTAIN COLLEGE SPEND ON THE AVERAGE 4.5

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Author: Christine Farr
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1. During the last week of the semester, students at a certain college spend on theaverage 4.5 hours using the school's computer terminals with a standard deviation of 1.8hours. For a random sample of 36 students at the college, find the probabilities that theaverage time spent using the computer terminal during the last week of the semester is(a)at least 4.8 hours(b)between 4.1 and 4.5 hours.ANSWER1: A_______________________B__________________________2. Ten randomly selected shut-ins were each asked to list how many hours oftelevision they watched per week. The results were:82 66 100 84 75 88 82 94 110 91a. Find x-bar b. Find sc. How many degrees of freedom will you use?Hint df = (n-1) when computing s1d. Determine the 99% Confidence interval estimate for the mean number of hours oftelevision watched per week by shut-ins. Assume the number of hours is normallydistributed.e. What is the length of the 99% CI? Note: Length = 2(E).f. Based on the Confidence interval, would you reject Ho: u = 75 at alpha=1% ?Please explainA_____________B_______________C____________D___________E_______F_______________________________________________________________3. A cab driver knows from experience that the number of fares hewill pick up in an evening is a random variable with u = 21 and standarddeviation = 3.4. Assuming that the distribution of this randomvariable can be approximated closely with a normal curve, find the probabilities that in anevening the driver will pick up (a) at least 30 fares (b) anywhere from 20 to 25 fares(including 20 and 25) . Since the number of fares is a discrete random variable, and weare using a normal curve, we will need continuity corrections on both parts a and babove. These continuity corrections are given below.a. P(At least 30 fares) = P(X greater than or equal to 30)= P(X>29.5) after continuitycorrection. If you don’t know what a continuity correction is, Please find this probabilityfor the given normal distribution: P(X>29.5).b. P(between 20 and 25 fares inclusive) = P(19.5<X<25.5) after a continuity correction.

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