statistics

TOPIC 5: DISCRETE PROBABILITY DISTRIBUTION 1. A test consists of 15 multiple choice questions with five choices for each question. As an experiment, you GUESS on each and every answer without even reading the questions. What is the probability of getting exactly 10 questions correct on this test? 2. In the mid-1990s, time magazine reported that 27% of the US Congress supported a tax cut as a means of stimulating the economy and increasing Tax revenues. Suppose at that time five members of congress were randomly selected for an interview and asked whether they supported the tax cut to stimulate the economy. Find the probability that: i. At least three of the five members were in favour of a tax cut. ii. Less than five members were in favour of a tax cut. ili. Not more than 3 members were in favour of the tax. iv. Find the mean of the above distribution v. Find the variance and standard deviation of the above distribution 3. The management of supermarket receives, on average, four requests per month to order items that the supermarket does not usually hold in stock. Find the probability that the supermarket receives: a. Exactly 5 such requests in a month b. No more than 3 such requests in a month c. At least 2 request in two months d. Find the mean of the above distribution e. Find the variance and standard deviation of the above distribution 4. A company that supplies ready-mix concrete receives, on average, six orders per day. What is the probability that, on a given day: a. only one order will be received? b. no more than three orders will be received? at least three orders will be received? i. What is the probability that, on a given half-day, only one order will be received? ii. What is the mean and standard deviation of orders received per day