# Normal Distribution on a Portfolio

1) The daily returns on a portfolio are normally distributed with a mean of 0.001 and a standard deviation of 0.002. What is the probability that the average return for the portfolio over the next 100 days exceeds 0.0015?

2) In May 1983, after an extensive investigation by the Consumer Product Safety Commission, Honeywell agreed to recall 770,000 potentially defective smoke detectors. The Commission suggested that about 40% of the Honeywell detectors were defective. However, Honeywell found only four defectives in a random sample of 2000 detectors and claimed that the recall was not justified. What is the probability of finding at most 4 defective detectors in a random sample of 2000 if, in fact, 40% of all detectors are defective?

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#### Solution Preview

1)

From the question,

mean return for one day = 0.0015

sd = 0.002

n = 100

Since the question is asking for the AVERAGE return over the next 100 days, use

z = (x - mean) / (sd / sqrt (n))

= (0.0015 - 0.001) / ...

#### Solution Summary

Formulas and computations are given for the problems. Answered in 176 words.