Reference no: EM132847564

Question 1: Find the probability and interpret the results. If? convenient, use technology to find the probability. During a certain week the mean price of gasoline was ?$2.704 per gallon. A random sample of 33 gas stations is drawn from this population. What is the probability that the mean price for the sample was between ?$2.683 and ?$2.723 that? week? Assume σ=?$0.05. The probability that the sample mean was between ?$2.683 and ?$2.723 is ?(Round to four decimal places as? needed.)

Question 2: The average math SAT score is 512 with a standard deviation of 111. A particular high school claims that its students have unusually high math SAT scores. A random sample of 50 students from this school was? selected, and the mean math SAT score was 556. Is the high school justified in its? claim? Explain. What is the Z score? ?(Round to two decimal places as? needed.)

Question 3: Your lumber company has bought a machine that automatically cuts lumber. The seller of the machine claims that the machine cuts lumber to a mean length of 8 feet ?(96 ?inches) with a standard deviation of 0.5 inch. Assume the lengths are normally distributed. You randomly select 37 boards and find that the mean length is 96.18 inches. a) Assuming the? seller's claim is? correct, what is the probability that the mean of the sample is 96.18 inches or? more?