You create a new recipe for a cake and need to figure out ex

You create a new recipe for a cake, and need to figure out exactly how long it takes to perfectly bake it at 350 degree F. To figure this out, you bake 25 cakes that take an average of 42 03 minutes to finish. You know that the standard deviation of cake baking time is 3 minutes. Provide a 92% confidence interval for cake baking time. A friend tells you he usually gets from his apartment to campus in less than fifteen minutes. He times himself every day for two weeks, and measures an average time of 13.4 minutes from his apartment to the front of Burruss Hall. \"He knows that due to variations in bus travel time, the standard deviation of his trip is five minutes. Test his claim that the average is less than 15 minutes using o = 0.04. A local casino claims that they have a new game where players actually break even on average. You play the game to test their claim. After ten games, you are up fifteen dollars, hut after playing 30 games you calculate a z-score of -2.44. Assume that sigma = $3 for one round of this new game. How much money did you make/lose in the last 20 games? What is the p value for your test. You want to know the average GPA of Virginia Tech students to see how yours compares. You take a sample of students, and find that they have an average GPA of 2.83. You know that the standard deviation of GPA is 0.8, and calculate a 95% confidence interval of (2.55, 3.11). How many students did you sample?

Solution

The average is 42.03 min

The sample size is 25.

The standard deviation is 3 min

The 92% CI is:

42.03 +/- (3)(1.75)/sqrt(25) = 40.98 to 43.08 minutes for baking time.