# Statistics Problem Set: Confidence Level

1) For the following sequence: 2,4,7,3,9,4,7,11 find the range, mode, median, mean, IQR, standard deviation, variance and whether it is normally distributed (with explanation)

2) An investor wants to assess at confidence level of 98% if a medicament can improve the marks of students. He notices that for the following daily dozes: 2,2.5,3,4.5,7 mg, the improvement over the students that studied the same but took no mental boosters were of: 3,4,4.6,6, 8.5 percent. At a confidence interval of 99%, what results would you expect for the students who take a daily dose of 6.5 mg? show full calculations.

3) A T 95 tank weighs 75 tons. A businessman wants to buy a couple of thousand tanks for hunting expedition in Texas. He will buy only if the tanks are really as specified and refuse to buy them if they statistically they weigh less. He takes a sample of 8 tanks and finds their average weight at 74.7 tons with a standard deviation of 0.3 tons. He wants to use a significance level of 2%. What will be his best course of action. Show all the work and justify your answer.

4) A car has a gas mileage of 500 miles per gallon of gasoline, with a standard deviation of 10 miles per gallon. What would be the gas mileage of the top 40% of such cars? What would be the mileage range for 70% of the cars? What %of cars will have a mileage of 530 miles per gallon of less?

5) The probability that a student answers a multiple question correctly is 27%, in an exam with 6 questions. What would be the probability the students answers correctly at random: no question, all questions, 6 questions, less than two and more than 4 questions? Answer individually all these questions, show all the work and explain your logic.

6) Mr. G. just won the jackpot with one ticket. He chose correctly 6 numbers out of 52 numbers and 2 stars our out of 12 stars. What was his probability of winning when he bought the ticket? Show full work and explain your answer.

#### Solution Preview

1. Please refer to the excel attachment for the calculations.

2. Please refer to the excel attachment for the calculations.

3. Null Hypothesis: The mean weight is greater than or equal to 75 tons.

H0: u >= 75

Alternate Hypothesis: The mean weight is less than 75 tons.

H1: u < 75

Let us ...