Can you help me with the binomial probability distribution? Please see instructions in the two images. Thank you.

Binomial Probability Distribution 1. Explain in your own words the importance of studying the binomial probability distribution. 2. Next, the probability distribution of a random variable is presented x. f (x) 20 0.38 25 30 0.15 35 0.37 a) What is presented in the table, is it a probability distribution? Explain. b) What is the probability that x = 35? c) What is the probability that x is less than or equal to 25? d) What is the probability that x is greater than 30? 3. Next, a probability distribution is presented. X Probability f (I 0 ).10 0.15 2 3 0.20 0.15 0.10 a) Find P (2). What is the expected (average) value of the number of services? What is the variance of the number of services? d) What is the standard deviation? 4. The probability distribution of the ratings established by employees on the relationship they have with their supervisors' ranges from 1 (poor) to 5 (excellent) Qualification of Supervisor Supervisor B the employee's A f (x) relationship with f (x) the supervisor (x) 0.05 0.04 0.09 0.10 0.03 0.12 0.42 0.46 0.41 ).28 a) What is the expected (mean) value of the securities offered to Supervisor A's rating? What is the expected (mean) value of the securities offered to Supervisor B's rating? Calculate the variance of the values offered to the rating of supervisor A. Calculate the standard deviation of the values offered for Supervisor B's rating. Compare satisfaction with Supervisor A with satisfaction with Supervisor B.5. Use the binomial distribution table to find the binomial probabilities for these cases: ) n = 10, p =1, k=3 b) n =14, p =.6, k=7 c) n = 25, p =.5, k = 14 6. Consider a binomial experiment with n = 20 and p = 0.70. Use the binomial formula to calculate: ) P(x = 15) b) mean variance d) standard deviation 7. 35% of YALE University students use their own car to get to college. What is the probability that, in a sample of 15 students, four (4) students use their own car? (Use the binomial formula to solve the exercise). 8. 40% of Americans traveling by car search for gas stations and grocery stores that are near or visible from the road. Suppose a random sample of n = 25 Americans who travel by car are asked how they determine where to stop to buy food and get gas. Let x denote the number of the responding sample looking for gas stations and grocery stores that are near or visible from the highway. (Use the binomial formula to solve the exercise). Answers: a) What is the mean if x = 10? b) What is the variance of x? c) Calculate the interval a + 20. d) What values of the binomial random variable x fall in this interval