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. a) Find the probability that exactly 14 survive. b) Find the probability that at least 10 survive. c) Find the probability that at most 16 survive. d) Find the mean and variance of the number that survive.

a)

b)

c)

d)

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

The probability mass function for the Binomial distribution is given as:

Where (nCx) means combinatory and it's given by this formula:

Part a

For this case we want this probability:

And using the mass function we have this:

Part b

For this case we want this probability:

And we can find this using the complement rule:

And if we replace we got:

Part c

For this case we want this probability:

And we can use the complement rule like this:

And if we replace we got:

Part d

The expected value is given by:

a 270° rotation about point p says on e d g e n u it y (had to space it out because it says it's a misspelling so i couldn't submit it

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step-by-step explanation: