Statistics and Probability Answers

A discrete random variable has probability mass function, P(X = n) =

135 UB students were surveyed and asked how many hours a week they spent studying. The results are in the table below?
Less than 5hrs (5 to10hrs) (More than 10) Total

Male (M) 25 25 20 70

Fmale (F) 20 30 15 65

Total 45 55 35 135

a) Complete the joint and marginal probability.

b) Find the probability that a student studied 5 to 10 hours.

c) Find the probability that a student is a male and spends less than 5 hours studying.

d) Find the probability that a student is a female or spends more than 10 hours studying.

e) Find the probability that a student spends more than 10 hours studying given that the student is a female?

f) Find the probability that a student is a male given that he spends less than 5 hours studying.

Are the following statistical statements sometimes, always or never true? If they are only sometimes true, give examples of conditions under which they are true and under which they are false. Is there some meaningful sense in which they might be 'usually' true or false? Be sure to be clear about your statistical assumptions in each case, especially in those which have a real-life basis.
1. Half of the students taking a test score less than the average mark.

The mean number of errors due to a bug occurring in a minute is 0.0001. What is the
probability that no error will occur in 20 minutes

The average mark of candidates in an aptitude test was 128.5 with a standard deviation of 8.2. Three scores extracted from the test are; 148, 102, 152. What is the average of the extracted scores that are extreme values (outliers)?

In a bolt manufacturing factory, machines A,B, and C produce 25%, 30% and 45% of the total output, respectively. Of their outputs, 7%, 6% and 4% are defective bolts, respectively. If a bolt drawn at random from the production is found to be defective, what is the probability that it was manufactured by machine C?

Emmanuel is given a multiple-choice exam with ten questions and each question with five possible answers. He decided to guess randomly for each question. What is the probability that he will get at least six questions correct

The average mark of candidates in an aptitude test was 128.5 with a standard deviation of 8.2. Three scores extracted from the test are; 148, 102, 152. What is the average of the extracted scores that are extreme values (outliers)?

Suppose that at a busy traffic junction, the probability p of an individual car having an accident is 0.0001. During a certain part of the day, 100 cars pass through the junction. What is the probability of two or more cars being involved in an accident within this period?

Raymond is a basketball player who takes four independent free throws with 70% probability of getting a basket on each shot. Let X be the number of baskets Raymond gets. Find the probability that he gets exactly 2 baskets, to 3 decimal places.