stastitics problem

Project Description:

consider a population data set of student's final exam grades from a large stats class. specifically, the number of students in the class is n = 100.

the population data set has the following characteristics:

a. a population mean value of 78.

b. a population standard deviation of 5.

c. the data set is dramatically skewed-left.

suppose you were to randomly sample from this population of n = 100, a sample size of n = 45. from your sample of 45 you calculate a sample mean (denoted as x-bar). now, suppose you were to repeatedly draw samples of size n = 45 and each time you calculated the sample mean for those 45 students.

[1] write the formula necessary to calculate how many unique samples (combinations) of n = 45 can be drawn from a population of n = 100.

[2] if you were to take all possible samples of size n = 45 from the population, and calculated the sample mean for each sample, what shape would the sampling distribution (i.e., the distribution of sample means) take? make sure to explain your answer here.

[3] what would the mean of the sampling distribution equal?

[4] what would the standard deviation of the sampling distribution equal? (the standard deviation of a sampling distribution is also called the "standard error")

[5] what is the probability of getting a sample mean greater than 80 from a sample of n = 45?

[6] a student at the 90th percentile has approximately what grade?
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