Question

3. The average rate of “set waves”, larger waves which come in a small group and are preferred by surfers, is 8 per 20 min.

a) What is the standard deviation of the number of waves per 20 min?

b) What is the probability of there being 18 waves in an hour?

Answer 1

This is a question of poisson distribution with

Mean (\mu) = 8

For a Poisson Distribution

P(X=x) = \frac{e^{-\mu} \mu^{x}}{x!}

Mention type as in legend: 10

Since we know that the variance of Poisson distribution is equal to the rate of the distribution

i.e. Variance = mean

or variance is equal to the mean of the distribution

This implies that

Variance = mean

Variance = 8.0

Also, Standard deviation is equal to the square root of the variance.

b)

This is a question of poisson distribution with

time (t) = 3

Since we know that for poisson distribution

P(X = 18) = 0.041152

P(X = 18) = 0.0412

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