A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a tank containing this concentration of chemical in water. Find the mean and variance of the number that survive.

Mean: 16

Variance: 3.2

Step-by-step explanation:

For each fish, there are only two possible outcomes. Either they survive, or they do not. The probability of a fish surviving is independent from other fishes. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

The variance of the binomial distribution is:

A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours.

This means that 80% survive, so

The mean is:

The variance is:

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step-by-step explanation: