I know the answer for question 1A) .05B) mean=2C)sd=1.225 But the rest I have no idea what to do. I need help with d-g. Please show work on a piece of paper.For question 5Please show detail as well.Will tip:)Thank you!

Question 1. (35 points) The table below reports the distribution of scores on the AP Statistics Exam in 2014. Let X be the score for a randomly selected student. a. Find P(X = 5). (3 points) b. Find the mean for X. (4 points) c. Find the standard deviation for X. (6 points) d. A score of three or above on the AP Exam is considered passing. If five students that took the exam are randomly selected, what is the probability that exactly two of them passed? (6 points) e. What is the probability that at most four of the five students passed? (6 points)00 T-Mobile Wi-Fi as 10:41 PM c @ >B 22% E Done Exam 2pdf LT] -- 20f6 d. A score of three or above on the AP Exam is considered passing. If five students that took the exam are randomly selected, what is the probability that exactly two of them passed? (6 points) e. What is the probability that at most four of the five students passed? (6 points) f. If 500 students that took the exam are randomly selected, what is the expected number of students that passed? (3 points) 9. What is the probability that more than 160 out of the 500 students passed? (7 points)Question 1. (35 points) The table below reports the distribution of scores on the AP Statistics Exam in 2014. Let X be the score for a randomly selected student. a. Find P(X = 5). (3 points) b. Find the mean for X. (4 points) c. Find the standard deviation for X. (6 points) d. A score of three or above on the AP Exam is considered passing. If five students that took the exam are randomly selected, what is the probability that exactly two of them passed? (6 points) e. What is the probability that at most four of the five students passed? (6 points)d. A score of three or above on the AP Exam is considered passing. If five students that took the exam are randomly selected, what is the probability that exactly two of them passed? (6 points) e. What is the probability that at most four of the five students passed? (6 points) f. If 500 students that took the exam are randomly selected, what is the expected number of students that passed? (3 points) 9. What is the probability that more than 160 out of the 500 students passed? (7 points)Question 5. (12 points) A sociologist wants to construct a 90% confidence interval for the proportion of children aged 8-10 living in New York who own a cell phone. a. What sample size is needed to ensure that the length of the confidence interval does not exceed 0.04? (8 points) b. If the sociologist wants to construct a 97% confidence interval with the same margin of error, would the necessary sample size be larger, smaller, or about the same? Explain. (4 points)