We have been told that in history, the one-year returns follow approximately the normal distribution. Given that the one-year return for the S&P 500 was +27% (that is, 0.27) and its S.D (standard deviation) is 20% (that is, 0.2). (i) Determine the probability that a stock in the S&P 500 gained 30% or more last yearrrrr? (ii) DEtermine the probability that a stock in the S&P 500 lost 10% or more last year? (iii) Determine the probability that a stock in the S & P lost 14% or more last year?

T7.12. The amount that households pay service providers for access to the Internet varies quite a bit, but the mean

Answer the three following questions a, b, and c. Taxes: The Internal Revenue Service reports that the mean federal income tax paid in the year 2010 was $8040. Assume that the standard deviation is $4700. The IRS plans to draw a sample of 1000 tax returns to study the effect of a new tax law.

Most exhibition shows open in the morning and close in the late evening. A study of Saturday arrival times showed that the average arrival time was 3 hours and 48 minutes after the doors opened, and the standard deviation was estimated at about 47 minutes. Assume that the arrival times follow a normal distribution.   (a) At what time after the doors open will 89% of the people who are coming to the Saturday show have arrived? (Round your answer to the nearest number of minutes.) minutes after doors open(b) At what time after the doors open will only 17% of the people who are coming to the Saturday show have arrived? (Round your answer to the nearest number of minutes.) minutes after doors open(c) Do you think the probability distribution of arrival times for Friday might be different from the distribution of arrival times for Saturday? Explain your answer.