A corn farmer has observed the following distributions for the numbers of ears of corn for per cornstalk Ears of corn 1,2,3,4 probability .3 , .4, .2, .1, Part a : how many ears of corn does he expect on average for each stalk? Round to the nearest tenths place Part b: the small farm is growing 100 stalks to sell corn at a local vegetable stand. If each ear of corn can be sold for 0.50$ how much money can they expect to make from one harvest? Question B: A major newspaper once reported that 74% of airline passengers prefer to sleep on long flights rather than watch movies or read consider randomly selecting 25 passengers from a particular long flight. Part a: on average how many of the 25 selected passengers will then use paper expect to sleep on a long flight A.18 B.18.5 C..19 D.19.5 Part B what is the probability that exactly 20 of those selected passengers prefer sleeping A- Almost 0% B-8.9% C-15.3 D-33.6 E-81.7 Part C: what is the probability that all passengers selected prefer to sleep on the long flight A- almost 0% B-8.9% C-15.3% D-33.6% E-81.7% The probability distribution of a random variable X is defined as follows X= 0,1,2,3,4 Probability=0, 0.3, 0.1 , 0.3, 0.3 The above distribution (responses: is , is not) ________ a valid probability model because ______ ( responses: the expected value is greater than 1, the sum of the probabilities equal to 1, The expected value is less than 1, the difference of the probabilities is equal to 1) ________ Part B: the expected value of the probability distribution is ( Responses: 2.0, 2.5, 2.6, 0.2) ______ Part C: the probability of x=5 is ( responses: 0,1 ) Part D: the probability that X>0 is (responses 0,1) Part E: let X represent the average number of televisions per household in a neighborhood how many televisions can we expect 50 households to have all together 5. Select all of the statements that represent properties of a binomial distribution A- all of the trails are identical B-is trial has only two possible outcomes (a success and a failure) C-The probability must remain the same for each trial D-the probability of success may change from trial to trial E- The purpose of the experiment is to determine the probability of a certain number of successes in n trials F- The purpose of the experiment is to determine the probability of a success happening by a certain trial Question 7 Assume the probability that you make any sale to any given customer is 0.25 find the following probabilities round to the nearest hundredth. Part A : P (make your first sale to the fifth customer)= _____ Part B: P (make your first sale to the first or second customer) =