Question

Suppose that for all Miami University STA 261 students, the average distance that they live from campus is 12.2 miles with a standard deviation of 8.0 miles. A random sample of 49 Miami university STA 261 students was taken, and the sample average distance that they live from campus was calculated.

a. what is the shape of the population distribution? Briefly explain your response

b. What is the probability that a randomly selected MU STA 261 student lives at least 10 miles from campus?

c. What is the probability that the sample average will have a value of at least 10 miles?

Answer 1

a. what is the shape of the population distribution? Briefly explain your response

Normally distributed as per central limit theorem

The central limit theorem states that the distribution of sample means approximates a normal distribution as the sample size gets larger (assuming that all samples are identical in size), regardless of population distribution shape.

Said another way, CLT is a statistical theory that states that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.

b.

c.