During a marksmanship exercise, every participant fires at a target until he/she hits the target once.  You hypothesize that all applicants are equally proficient (i.e., have the same probability of hitting the target) and that the hit probability does not vary by shot (i.e., all participants have the same hit probability on all shots). Furthermore the shots are independent across individuals and independent across shots for the same individual. You believe that the hit probability is 0.4. There are 100 participants.  Below is the results of the exercise.  It specifies how many of the participants first hit the target after the given number of shots. For example 42 hit the target on the first shot, 15 first hit the target on the third shot,  20 take at least 5 shots to first hit the target #Shots to first hit target        #Participants 1 42 2 14 3 15 4 9 5 or more 20   Perform the appropriate hypothesis test at the alpha = 0.05 level to evaluate your hypothesis described in first paragraph.  Report  the p-value to at least at least 2 significant digits

At a certain large company, the floor manager reviewing inventory and production. She ultimately comes to the decision that a product should be continued if it sold 150,000 times over the previous year. In addition, the product is considered “popular” if it receives at least 100 mentions by the local press over the past year. An analyst is hired to help with the analysis.  The analyst determines that the probability of sales exceeding 150,000 was 0.331, the probability of 100 or more mentions was 0.162, and the probability that a product both sold 150,000 items, and was also ‘popular’ is 0.064. What is the probability that a randomly selected product either sold the requisite 150,000 items, or that it is ‘popular’? Again, phrase your answers in terms of probability variables (e.g. P(X) = ...,  P(Y)=... etc.) If we are told that an item has indeed reached the threshold of 100 mentions in the press, what is the probability of it selling 150,000 times?  Thought Question: Where would the…

Suppose you model a game of chance with a discrete probability distribution. Let X be the net amount of money or lost by the player. Let pX be the probability of the corresponding outcome. The three events are as follows: There is a 23% chance the player wins 7 dollars. there is a 38% chance the player loses 4 dollars. there is a 39% chance the player breaks even. COMPLETE THE TABLE BELOW TO MODEL THE SCENARIO X            PX)

The probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.10. Each student does homework independently. In a statistics class of 50 students, what is the probability that at least 5 will do their homework on time?