Math Stats Exam Help

Final Exam - Review 1 M243, Sum ’19

Q1 A fair coin is tossed three times.

(a) Write out the sample space of this experiment.

(b) Let X be the number of heads that occur. Give the probability distribution of X by filling out the table below.

x 0 1 2 3 P(X = x)

(c) What is the probability that at least two heads will occur given that at most two heads have occured?

Q2 Scores on the Medical College Admission Test (MCAT) are approximately Normal, with a mean score of 25 and a standard deviation of 6.4.

(a) If you choose a student at random, what is the probability that the student’s score is between 20 and 30?

1

Final Exam - Review 1 M243, Sum ’19

(b) You sample 25 students. What is the distribution of the sample mean X?

(c) What is the probability that the mean score of your sample is between 20 and 30?

(d) How large of a sample must you take so that the margin of error of a 98% confidence interval for the mean exam score is at most 0.727?

Q3 In the Framingham Heart Study, 3,539 adult participants had their systolic blood pressure mea- sured, finding a sample blood pressure of x = 127.3 with standard deviation s = 19.0. Find a 99.9% confidence interval for the mean systolic blood pressure of all adults.

2

Final Exam - Review 1 M243, Sum ’19

Q4 A Person seems to get a disproportionate amount of sixes when rolling a six-sided die for a game.

(a) Assuming the die is fair, what is the probability of rolling a six?

(b) During 29 rolls, the person gets 8 sixes. Is this sufficient evidence that the person is cheating (i.e. that the die is not fair)?

Q5 An urn contains twelve chips, numbered 1 through 12. One is drawn at random. Let A be the event that the number is divisible by 2 and B be the event that the number is divisible by 3.

(a) Find P(A or B).

(b) Are A and B independent? Explain.

3

Final Exam - Review 1 M243, Sum ’19

Q6 An experiment finds that out of a group of 9 people, 6 of them like chocolate.

(a) Explain why we should not use a 95% large sample confidence interval for the proportion of people that like chocolate.

(b) Find the 95% plus-four confidence interval for the people who like chocolate.

Q7 A study of the effect of exposure to colour (red or blue) on the ability to solve puzzles used 42 subjects. Half of the subjects (Group 1) were asked to solve a series of puzzles while in a red- coloured environment. The other half (Group 2) were asked to solve the same series of puzzles while in a blue-coloured environment. The subjects in Group 1 had a mean time for solving the puzzles of 9.64 seconds with standard deviation 3.43 seconds. The subjects in Group 2 had a mean time of 13.84 seconds with standard deviation 8.65 seconds. Is there a significant difference (α = 0.05) in the mean time taken to solve the puzzle between people in red-coloured and blue- coloured environments?

4

Final Exam - Review 1 M243, Sum ’19

Q8 Isabelle is currently running two scams out of a bogus Facebook page. She estimates that the chances of the first one leading to her arrest are one in ten; the “risk” associated with the second is more like one in thirty. She considers the likelihood that she gets busted for both to be 0.0025. What are Isabelle’s chances of avoiding incarceration?

Q9 Two samples of 160 graduate students are taken. For the first sample, the mean quantity of coffee drunk per was was 355ml with standard deviation 97ml, while for the second sample the mean was 320ml with standard deviation of 88ml. Is there evidence of a difference in the mean quantity of coffee drunk per day between the two samples?

5