The workers union at a certain university is quite strong. About 96% of all workers employed by the university belong to the workers union. Recently the workers went on strike, and now a local TV station plans to interviews a sample of 10 workers, chosen at random, to get their opinions on the strike.
A) Estimate the number of workers in the sample who are union members by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable).Do not round your response.
B) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

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 the expected value is given by:

Part b

For this case the standard deviation is given by:

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".

Solution to the problem

Let X the random variable of interest "number of workers in the sample who are union members", 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 the expected value is given by:

Part b

For this case the standard deviation is given by:

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step-by-step explanation:

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