Discussion:
Q1) In a class there are 60 students. The mean exam score is 70 and the standard deviation is 5. Assume symmetric distribution of the scores.
(i) What can you say about the number of students that have scores between 55 and 85?
(ii) What can you say about the number of students who have scores between 60 and 80?
Q2) Let Z have a standard normal distribution. Find the following probabilities:
a) P(Z is between -2.52 and 2.67)
b) P( Z is more than -1.26)
Q3) A gas company president for a particular city is interested in the proportion of homes heated by gas. Historically, the proportion of homes heated by gas has been 65%. A sample of 75 home was selected and it was found that 44 of them heat with gas. Perform the appropriate test of hypothesis to determine whether the proportion of home heated by gas has changed. Test using the 5% level of significance.
Q4) A class had a mean of 67 in the final exam and a standard deviation of 5. The class has more poorly performing students than those who perform well. What can you say about the percentage of students who have scores between 57 and 77?
Q5) Tough Road Tire Company wants to test its new brand of tires. The engineering department of the company claims that the new tires last more than 40,000 miles in the average. A sample of 40 tires was tested and found that the average number of miles they lasted for the sample was 43,200 miles with a standard deviation of 8000 miles. At the level of significance 0.05, can the company claim that the tires last an average of more than 40,000 miles?
Q6) A weight loss program measured the weights lost by 12 participants. For this sample of 12 participants the mean weights lost was 15.2 pounds and the standard deviation was 5.3 pounds. Find the 95% confidence interval for the average (mean) weight lost by the participants of this program. Assume that the weights lost by the participants follow a normal distribution.