# STAT-202 Graduation Make-up Exam Solved, No Plagiarism

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A recent study by the Ercan Taxi Drivers Association showed that the mean fare charged for service from Alagadi Beach to Ercan Airport is \$20 and the standard deviation is \$4. We select a sample of 20 fares (Assume that population is normally distributed). What is the probability that the sample mean is between \$18.00 and \$22.00?
2. The average IQ of a random sample of 25 students at a college is 110. If the distribution of the IQ at the college is known to be normal with a standard deviation of 10. Find the 95% confidence interval for the unknown mean IQ for the entire student body at the college.
3. A firm sells detergent packed in two plants. From past experience, the firm knows that the amount of detergent in the boxes packed in the two plants is normally distributed. The firm takes a random sample of 25 boxes from the output of each plant and finds that the mean weight and
standard deviation of the detergent in the boxes from plant 1 is 1064 g (gram) and 100 g, respectively. For the sample in plant 2, the mean is 1024 g and the standard deviation is 60 g.
a) Can the firm claim with a 95% level of confidence that the boxes of detergent from plant 1 contain more than 1000 g?
b) Test at the 95% level of confidence that the amount of detergent in
the boxes of both plants is the same.
4. The lifetime of an electronic component is known to be normally distributed with a mean of 1000 h (hour) and a standard deviation of 80 h. What is the probability that a component picked at random from the production line will have a lifetime
a) Between 1120 and 1180 h?
b) Above 975 h?
c) Sketch the normal and the standard normal distribution for this problem and shade the area corresponding to part b).
5. The Policy of the Suburban Transit Authority of Country XYZ is to add a bus root if more than 60% of the potential citizens indicate they would use the particular root. A sample of 100 citizens revealed that 70 would use the proposed root. Will the Suburban Transit Authority add this bus root? Use the 0.05 (5%) level of significance.

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A recent study by the Ercan Taxi Drivers Association showed that the mean fare charged for service from Alagadi Beach to Ercan Airport is \$20 and the standard deviation is \$4. We select a sample of 20 fares (Assume that population is normally distributed). What is the probability that the sample mean is between \$18.00 and \$22.00?
2. The average IQ of a random sample of 25 students at a college is 110. If the distribution of the IQ at the college is known to be normal with a standard deviation of 10. Find the 95% confidence interval for the unknown mean IQ for the entire student body at the college.
3. A firm sells detergent packed in two plants. From past experience, the firm knows that the amount of detergent in the boxes packed in the two plants is normally distributed. The firm takes a random sample of 25 boxes from the output of each plant and finds that the mean weight and
standard deviation of the detergent in the boxes from plant 1 is 1064 g (gram) and 100 g, respectively. For the sample in plant 2, the mean is 1024 g and the standard deviation is 60 g.
a) Can the firm claim with a 95% level of confidence that the boxes of detergent from plant 1 contain more than 1000 g?
b) Test at the 95% level of confidence that the amount of detergent in
the boxes of both plants is the same.
4. The lifetime of an electronic component is known to be normally distributed with a mean of 1000 h (hour) and a standard deviation of 80 h. What is the probability that a component picked at random from the production line will have a lifetime
a) Between 1120 and 1180 h?
b) Above 975 h?
c) Sketch the normal and the standard normal distribution for this problem and shade the area corresponding to part b).
5. The Policy of the Suburban Transit Authority of Country XYZ is to add a bus root if more than 60% of the potential citizens indicate they would use the particular root. A sample of 100 citizens revealed that 70 would use the proposed root. Will the Suburban Transit Authority add this bus root? Use the 0.05 (5%) level of significance.

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