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Statistical Inference

Problem 1

The daily return of a certain stock is normally distributed with a mean of 0.30% and a standard deviation of 2.50%.

a)Find the probability that the return on a randomly selected day is negative.

State the Excel function (specifying all inputs) that will compute this probability.

b)Find the level, L, such that there is a 20% chance that the daily return on a randomly selected day exceeds L.

State the Excel function (specifying all inputs) that will compute L.

c)Find the probability that the average return over 4 randomly selected days is negative?

State the Excel function (specifying all inputs) that will compute this probability.

d)Find the probability that the return is negative on each of 4 randomly selected days? (Joint probability)

e)Find the level, M, such that there is a 20% chance that the average return over 4 randomly selected days exceeds M.

State the Excel function (specifying all inputs) that will compute M.

Problem 2

SmithCo is a supplier to many brand name makers of mobile phones.SmithCo manufactures the external shells that enclose mobile phones.The strength of a shell is measured by applying increasing pressure to the shell and recording the pressure at which the shell breaks.Shell strengths are approximately normally distributed.A random sample of 10 shells made by SmithCo showed an average strength of 45.0 pounds and a standard deviation of 2.0 pounds.We wish to construct a 90% confidence interval for the mean shell strength.

a)State the appropriate z-value or t-value that must be used.

b)State the confidence interval in the form a b.

c)State the confidence interval in the form [c, d].

d)Determine the sample size required to estimate the mean strength within one pound with a 90% confidence level and assuming that the population standard deviation is 2 pounds.