Question

. The average return on the stocks in the S&P 500(stock with 500 companies) over the past 90 years has been 9.8% and the standard deviation has been about 15%.

(a) Infer that you take a simple random sample of 50 companies from the S&P 500. You calculate an average return of X¯ for this sample. What is the distribution of X¯?

(b) Continuing from part (a), for a simple random sample of 50 companies, what is the probability that the average return in this sample will be lower than 9.9%?

Answer 1

Let X : return on the stocks in the S&P 500(stock with 500 companies) over the past 90 years has mean = 9.8% and standard deviation = 15%

a) if n = 50 the sampling distribution of sample mean Xbar is

  xbar = 9.8% and  xbar = /√n = 15/√50 = 2.12%

b) P( xbar < 9.9) = P( xbar - )/(/√n) < (9.9-9.8)/2.12]

P(xbar < 9.9) = P( Z < 0.0472)

P(xbar < 9.9) = 0.5199