The Typical Computer Random-Number Generator Yields Numbers in a Uniform

question 186

Essay

The typical computer random-number generator yields numbers in a uniform distribution between 0 and 1 with a mean of 0.500 and a standard deviation of 0.289. (a) Suppose a sample of size 50 is randomly generated. Find the probability that the mean is below 0.300.
(b) Suppose a sample size of 15 is randomly generated. Find the probability that the mean is below 0.300. These two problems appear to be very similar. Only one can be solved by the central limit theorem. Which one and why?

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Definitions:

Sperm

Male reproductive cells designed to fertilize female eggs during sexual reproduction, carrying genetic material to the egg.

Locations

Specific places or positions within a given space or area.

Zygote

The initial cell formed when two gamete cells are joined by means of sexual reproduction, containing genetic information from both parents.

Gamete

A mature sexual reproductive cell, such as a sperm or egg, that unites with another cell to form a new organism.