Please only do that one that is incorrect Or isn't done Suppose that the amount of time that students spendstudying in the library in one sitting is normallydistributed with mean 40 minutes and standarddeviation 16 minutes. A researcher observed 47students who entered the library to study. Round allanswers to 4 decimal places where possible.a. What is the distribution of X? X - N(( 4016b. What is the distribution of æ? ¤ - N( 402.3338c. What is the distribution of > x? ) x - N(1880 v109.69d. If one randomly selected student is timed, findthe probability that this student's time will bebetween 41 and 42 minutes. 0.9956e. For the 47 students, find the probability thattheir average time studying is between 41 and 42minutes. 0.3465f. Find the probability that the randomly selected47 students will have a total study time morethan 1974 minutes. 0.2267g. For part e) and f), is the assumption of normalnecessary?Yes O No oh. The top 10% of the total study time for groups of47 students will be given a sticker that says"Great dedication". What is the least total timethat a group can study and still receive a sticker?0.1089Xminutes

(d) Obtain the probability that the student’s time will be between 41 and 42 minutes. The probability that the student’s time will be between 41 and 42 minutes is obtained below as follows: The probability that the student’s time will be between 41 and 42 minutes is 0.0278.(e) Obtain the probability that the student’s time will be between 41 and 42 minutes for a sample of 47 students. The probability that the student’s time will be between 41 and 42 minutes for a sample of 47 students is obtained below as follows: The probability that the student’s time will be between 41 and 42 minutes for a sample of 47 students is 0.1387.(f) Obtain the probability that the randomly selected 47 student’s will have a total study time more than 1974 minutes. The probability that the randomly selected 47 student’s will have a total study time more than 1974 minutes is obtained below as follows: The required probability is, The probability that the randomly selected 47 student’s will have a total study time more than 1974 minutes is 0.1949.