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.
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