17-09-2018

Problem 1. Consider the following data

Compute the following

• 1. The mean

  2. The median

  3. The mode

  4. First, second and third quartiles and the interquartile range

  5. The 20th percentile

Problem 2. Suppose a fair coin is tossed 2 times. Consider the following events

• • E1= the coin turns up heads on the first toss

  • E2= the coin turns up heads on the second toss

Solve the following

• 1. P(E1) and P(E1c) (use both counting sample points and the formula)

  2. P(E2) and P(E2c)

  3. P(E1∩E2)

  4. Use counting sample points and addition law to compute P(E1UE2)

  5. P(E1|E2)

  6. Are the two events independent?

Problem 3. In a given statistics class, half the students were female. It is also known that ⅔ of the students were business and economics majors, while the rest were psychology majors. It is further known that ⅓ of the girls are Business and economics majors. If I pick a student at random, compute the following probabilities:

• 1. That the student is female

  2. That the student is a business and economics major

  3. That the student is a psychology major

  4. That the student is female and psychology major

  5. That the student is a male and business major

  6. Given that the student I pick is a business major, what is the probability that the student is male

  7. Given that the student I pick is a psychology major, what is the probability that the student is female

  8. Are being a business major and being female independent events?

  9. Suppose it is not known that ⅓ of the girls are business majors, but instead that major of students is independent of their gender. Then what fraction of girls are business majors?