(1) For the following statement write the null hypothesis and the alternative hypothesis also label which one is the claim. A car manufacturer claims that their cars makes at least 35 miles per gallon of fuel.
(2) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 25 minutes. A random sample of 49 home delivery pizzas were collected. The sample mean was found to be 26.5 minutes and the standard deviation was found to be 4 minutes. Is there evidence to reject the managers claim at alpha= .05? Perform and appropriate hypothesis test , showing the necessary calculations and/or explaining the process used to obtain the results.
(3) A multiple choice exam contains 50 questions. Each question has 5 choices, one of which is correct. We are interested in knowing the probability guessing exactly 18 questions correctly. (a) Is this a binomial experiment? Explain how you know. (b) Use the correct formula to find the probability of guessing exactly 18 questions correctly out of the 50 questions. Show your calculations or explain how you found the probability.
(4) The monthly utility bills are normally distributed with a mean value of $130 and a standard deviation of $15.
(a) Find the probability of having a utility bill between 100 and 150
(b) Find the probability of having a utility bill less than $90
(c) Find the probability of having a utility bill more than $160
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