At a local fair, there is a game that offers cash prizes. To play the game, a colored ball is drawn at random from a big box and if the ball is gold, you win cash money. (The ball is put back in the box each time the game is played.) In the box, there are 9 gold balls out of a total of 300 balls. Suppose 100 people play the game.(a)What is the probability that exactly 4 people draw a gold ball? Calculate this probability using a binomial distribution. Round your answers to four decimal places.(b)Use the Poisson distribution to approximate the probability that exactly 4 people draw a gold ball. Round your answer to four decimal places.

Justin is a basketball player. The probability that he makes a half-court shot is 0.04. Suppose Justin shoots 130 half-court shots.(a)What is the probability that Justin makes exactly 6 of these half-court shots? Calculate this probability using a binomial distribution. Round your answers to four decimal places.(b)Use the Poisson distribution to approximate the probability that Justin makes exactly 6 of these half-court shots. Round your answer to four decimal places.

The winners of a carnival game draw a ticket from a box to determine their prize. Each winner draws a ticket and places it back into the box before the next draw. Every winner has a 28% chance of getting a pencil pouch, a 56% chance of getting a backpack, and a 16% chance of getting a gumball.The game operator wants to simulate what could happen for the next ten winners.So for each winner, she generates a random whole number from 1 to 100.She lets 1 to 28 represent a winner getting a pencil pouch, 29 to 84 a backpack, and 85 to 100 a gumball.Here is the game operator's simulation.Winner 1 2 3 4 5 6 7 8 9 10Random number 46 71 66 72 32 55 7 59 4 28In the simulation, which prize did each winner get?(a) Winner 4: (b) Winner 9: (c) Winner 10:

A park receives an average of 20 tourists per hour. Assuming that the arrival time of tourists follows a Poisson distribution, what is the probability that exactly 8 tourists will be received in any given hour?Round your results to four decimal places.

Twenty five individuals are randomly selected out of 100 shoppers leaving a local bedding store. Each shopper was asked if they made a purchase during their visit. Each of the shoppers has the same probability of answering yes to having made a purchase. The probability that exactly four of the twenty-five shoppers made a purchase could best be found by?Select one:a.using the normal distribution.b.using the binomial distribution.c.using the Poisson distribution.d.using the exponential distribution.e.using the uniform distribution.

Six coins are tossed 6,400 times. Using the Poisson distribution, find the approximateprobability of getting six heads x times.