Can you solve the question below? AP Statistics Unit 5: Sampling Distributions for ProportionsEmpodoltaniPeriod A S/M Date SubmittedU5 Lesson 3 Mastery CheckComplete this mastery check in your own handwriting and submit it for review, feedback and grading.Be sure to enter the date you are submitting this mastery check for the first time.If we take repeated samples of the same size n from a population with mean u, the samplingdistribution of will have the following characteristics:1) The shape of the sampling distribution depends on the shape of the populationdistribution. If the population is Normally distributed, the sampling distribution of willbe Normally distributed. If the population of distribution is non-Normal, the samplingdistribution of x will become more and more Normal as n increases.2) The mean of the sampling distribution of u = .3) The standard deviation of the sampling distribution is o; =%DNote: The formula for the standard deviation is exactly correct only if we are sampling from aninfinite population or with replacement from a finite population. When we are sampling withoutreplacement from a finite population, the formula is approximately correct as long as the 10%condition is satisfied. That is, the sample size must be less than or equal to 10% of thepopulation size.1. The times it takes 5th graders to complete a particular mathematics problem areNormally distributed with mean 2 minutes and standard deviation 0.8 minutes.a) Find the probability that a randomly chosen 5th grader will take more than 2.5minutes to complete the problem. Show your work.b) Suppose you give the problem to an SRS of 20 students. Sketch the samplingdistribution of x. Then use this distribution to determine the probability that themean time to complete the problem for the SRS of students is greater than 2.5minutes. Show your work.

Question

Accepted Answer

Given :
mean = 2
standard deviation = 0.8