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# Binomial, Normal & Uniform Probabilities

In a recent survey 35 percent indicated chocolate was their favorite flavor of ice cream. Suppose we select a sample of 10 people and ask them to name their favorite flavor of ice cream.
a. How many of those in the sample would you expect to name chocolate
b. What is the probability exactly four of those in a sample named chocolate
c. What is the probability four or more name chocolate

A recent report in USA Today indicated a typical family of four spends \$490 per month on food. Assume the distribution of food expenditures for a family of four follows the normal distribution, with a mean of \$490 and a standard deviation of \$90.
a. What fraction of the families spend more than \$30 but less than \$490 per month on food?
b. What fraction of the families spend less than \$430 per month on food
c. What fraction spend between \$430 and \$600 per month on food
d. What fraction spend between \$500 and \$600 per month on food

A tube of Listerine Tartar Control toothpaste contains 4.2 ounces. As people use the toothpaste, the amount remaining in any tube is random. Assume the amount of toothpaste left in the tube follows a uniform distribution. From this information, we can determine the following information about the amount remaining in a toothpaste tube without invading anyone's privacy
a. How much toothpaste would you expect to be remaining in the tube
b. What I the standard deviation of the amount remaining in the tube
c. What is the likelihood there is less than 3.0 ounces remaining in the tube?
d. What is the probability there is more than 1.5 ounces remaining in the tube

#### Solution Summary

The solution provides step by step method for the calculation of binomial, normal and uniform probabilities. Formula for the calculation and Interpretations of the results are also included.

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