Twenty-three percent of automobiles are not covered by...

Twenty-three percent of automobiles are not covered by insurance (CNN, February $23,$ 2006 ). On a particular weekend, 35 automobiles are involved in traffic accidents. a. What is the expected number of these automobiles that are not covered by insurance? b. What are the variance and standard deviation?

Twenty-three percent of automobiles are not covered by insurance (CNN, February $23,$ 2006 ). On a particular weekend, 35 automobiles are involved in traffic accidents.
a. What is the expected number of these automobiles that are not covered by insurance?
b. What are the variance and standard deviation?

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Key Concepts

Variance and Standard Deviation

The variance of a binomial distribution is found using the formula n*p*(1-p), which measures the spread of the distribution around its mean. The standard deviation is the square root of the variance, providing a scale for how much the number of successes is expected to deviate from the mean on average.

Binomial Distribution

The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success. It is applicable when there are exactly two outcomes for each trial, such as 'insured' or 'not insured', making it ideal for this type of probability problem.

Expected Value

The expected value in a binomial distribution is calculated using the formula n*p, where n is the number of trials and p is the probability of success (or the event of interest). This gives the average or mean number of successes over many repetitions of the experiment.

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