A Young Boy Is Fishing Off the End of a Dock

question 83

Essay

A young boy is fishing off the end of a dock. He estimates that for one out of every 15 times he casts his line, he gets at least a nibble from a curious fish. He is going to cast his line 50 times before he switches to toad hunting.
-Suppose that our fearless fisherman goes out early one morning and casts a total of 250 times. What are the mean and standard deviation of the number of times he should receive a nibble on his line?

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Definitions:

Sampling Distribution

The probability distribution of a statistic obtained through a large number of samples drawn from a specific population.

Simple Random Samples

A subset of a population where every member has an equal chance of being selected, ensuring unbiased representation.

Standard Error

A measure of the sampling variability of an estimator, indicating the uncertainty around the estimate of a population parameter.

Variance

A statistical measure that represents the dispersion or spread of data points in a data set.