Hello teacher, these are statistical questions, there are F-distribution, chi-square test, binomial distribution of these knowledge points, I hope the teacher can draw pictures and send me the solution process, thank you very much.

38. Assuming a two-candidate election, if a specic candidate receives at least 55% of the vote in the sample, that candidate will be forecast as the Winner of the election. If a random sample of 100 voters were selected, what is the probability that a candidate will be forecast as the winner when the population percentage of her vote is 50.1%? a. 0.8461 b. 0.1635 c. 0.8365 (1. none of the options 39. An orange juice producer buys oranges from a large orange grove that has one variety of orange. The amount of juice squeezed from these oranges is approximately normally distributed, with population mean of 4.70 ounces and standard deviation of 0.40 ounce. If a sample of 25 oranges is selected, the probability is 77% that the sample mean amount of juice will be lesser than what value? a. 5.1487 b. 3.1342 0. 4.7592 d. none of the options 41. A client wants to have 95% confidence of the population mean processing time to within more or less than 4 days with standard deviation of 25 days. What is the approximate sample size needed? a. 120 b. 140 c. 150 d. 170\f25. A survey was conducted with 300 customers of a shop. The number of customers that has bought a television is 80 and 240 customers are satisfied with the shop. Out of the customers who are satisfied, 64 of them bought a television. Given that A = satisfied with the shop and B = buy a television. Both A and B are independent. What is P(A | B) and P(A)? a. P(A B) = 0.5, P(B) = 0.5 b. P(A B) = 0.5, P(B) = 0.7 c. P(A| B) = 0.8, P(B) = 0.8 d. P(A | B) = 0.5, P(B) = 0.8