Solve and explain for me

Solve the following questions distribution 1. The number of connections on the internet during two-minute period is given by the following Number of times Proportion 0 0.1 0.2 2 0.1 3 0.4 minute period a. Determine the mean number of times a connection is made during a two-minute period 4 b. Determine the standard deviation of the number of times a connection is made during a two- 0.2 2 Abdullah is considering an investment in a company. He is interested in buying a number of shares of this company and keep them for one year. The price of a single share at this time is $16 and the forecasted price a year from today is given in the following table Price of stock in one year Probability 15 16 17 18 |19 0.15 0.20 0.26 a. Does the information above describe a valid probability distribution function? Justify 0.21 0.18 b. What is the variance and standard deviation of the stock price a year from today? 3. A packing company is inspecting a shipment of grapefruit by cutting 15 grapefruit selected at random. The company will accept all grapefruit if 14 or all of these 15 grapefruit are of quality. satisfactory quality. Suppose that 95% of the grapefruit of the shipment are of satisfactory (a) Write the probability distribution of the grapefruits that are of satisfactory quality in the sample of 15 grapefruit. (b) What is the probability that the shipment will be accepted? (i.e. the probability of 14 or 15 good grapefruits out of 15)? 4. A bag contains 7 English books and 5 Math books. Suppose that you randomly select 4 books from the bag. Let X be the number of Math books in these 4 books that will be selected from the bag. a. Write the probability distribution of X? b. What is the probability that you select two Math and two English books? 5. Ahmad must select two Management courses and 3 Math courses. If the catalog contains 5 management and 8 Math courses, how many ways can Ahmad complete his schedule? 6. Customers use an automatic teller machine at an average of 15 per hour. a. What is the probability that exactly 12 will use the machine in the next hour? b. What is the probability that at least one will use the machine in the next 20 minutes? 7. In a statistics class with 15 males and 13 females, five students are selected to put problems on the board. What is the probability that? a. 4 females are selected? b. at most one male is selected