You are up for a promotion at your work and you know that you needed to get at least 24.6 sales exactly this month to be set for the promotion. The average number of sales in your store was 24 with a standard deviation of 2 and a normal distribution. Based on this distribution what would be the likelihood you will be getting your promotion? Please provide a brief interpretation for the Z-score of the minimum number of sales you would need.

There is a new medication for diabetes, fifteen participants take the medication for fifteen days. The average blood glucose before taking the medication was 155 (population mean). The average blood glucose after taking the medication is 110. The standard deviation for the average glucose after taking the medication is 4.6. You want to evaluate if there is statistical evidence that there is a reduction in the mean glucose after taking the medication for 15 days. You must conduct a t-test. What is the t-statistic?

The mean score for first exam in your first organic chemistry class (section A) was 60, with a standard deviation of 5. Your score on the exam was 70. A. How many standard deviations above the mean is your score?

To celebrate the end of final exams you and friends head to a favorite downtown restaurant. You find a street parking spot with a maximum of two hours. If you stay longer than two hours, you risk having your car towed away. No one has a watch or cellphone but you remember that the average time you spent at the same restaurant over your previous 16 visits is 1.5 hours, and you estimate the sample standard deviation to be about 20 minutes. You also need to factor in that it takes 8 minutes to walk to the restaurant and 8 minutes to walk back to your car (you are very certain about these two durations). (a) One of your friends is really worried that you won’t get back to the car in time and so the car might be towed away! Does your friend have good reason to be worried? Test at a 5% significance level whether the mean total time will be less than two hours. (b) You decide to leave the car parked at the street spot but it gets towed. What type of error have you committed?

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find P40​, which is the IQ score separating the bottom 40​% from the top 60​%. Round your answer to nearest tenth.

Joe went bowling in two leagues. In the first league, the mean bowling score is 167 with a standard deviation of 44. In the second league the mean bowling score is 180 with a standard deviation of 36. If he bowls a game of 201 in both leagues, in which league is this score the best in comparison to other bowlers? Explain.