A group of 20 students have been on holiday abroad and are returning to Norway. In the group, there are 7 who have bought too much alcohol on duty-free and none of them informs the customs officers about it. Customs officers randomly select 5 people from these 20 students for control. We let the variable X be the number of students among the 5 selected who have bought too much alcohol. (a) What type of probability distribution does the variable X have? Write down the formula for the point probabilities. (b) What is the probability that none of those checked has bought too much? (c) What is the probability that at least 3 of the 5 controlled students have bought too much? (d) What is the expected value and standard deviation of X? (e) What is the probability that only the third person being checked has bought too much?
A group of 20 students have been on holiday abroad and are returning to Norway. In the group, there are 7 who have bought too much alcohol on duty-free and none of them informs the customs officers about it. Customs officers randomly select 5 people from these 20 students for control.
We let the variable X be the number of students among the 5 selected who have bought too much alcohol.
(a) What type of probability distribution does the variable X have? Write down the formula for the point probabilities.
(b) What is the probability that none of those checked has bought too much?
(c) What is the probability that at least 3 of the 5 controlled students have bought too much?
(d) What is the expected value and standard deviation of X?
(e) What is the probability that only the third person being checked has bought too much?
Step by step
Solved in 3 steps with 3 images
