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# Probability

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1. An economist wishes to estimate the average family income in a certain population. The population standard deviation is known to be \$4,500, and the economist uses a random sample of size = 225.

a. What is the probability that the sample mean will fall within \$800 of the population mean?
b. What is the probability that the sample mean will exceed the population mean by more than \$600.

Please provide full detail including how the z-table lookup is determined.

2. The article "Reliability of Domestic Waste Biofilm Reactors" (J. of Envir. Engr., 1995: 785-790) suggests that substrate concentration (mg/cm^3) of influent to a reactor is normally distributed with &#61549; = 0.30 and &#61555; = 0.06.

a. What is the probability that the concentration exceeds 0.40?
b. What is the probability that the concentration is at most 0.25?
c. How would you characterize the largest 10% of all concentration levels?