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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> A bank accepts rolls of pennies and gives 50 cents credit to a customer without counting the contents. Assume that a roll contains 49 pennies 30 percent of the time, 50 pennies 60 percent of the time, and 51 pennies 10 percent of the time. <ul><...") |
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A bank accepts rolls of pennies and gives 50 cents credit to a customer without counting the contents. Assume that a roll contains 49 pennies | |||
without counting the contents. Assume that a roll contains 49 pennies | |||
30 percent of the time, 50 pennies 60 percent of the time, and 51 pennies | 30 percent of the time, 50 pennies 60 percent of the time, and 51 pennies | ||
10 percent of the time. | 10 percent of the time. | ||
<ul><li> Find the expected value and the variance for the amount that the bank | <ul style="list-style-type:lower-alpha"><li> Find the expected value and the variance for the amount that the bank | ||
loses on a typical roll. | loses on a typical roll. | ||
</li> | </li> | ||
Latest revision as of 23:02, 14 June 2024
A bank accepts rolls of pennies and gives 50 cents credit to a customer without counting the contents. Assume that a roll contains 49 pennies 30 percent of the time, 50 pennies 60 percent of the time, and 51 pennies 10 percent of the time.
- Find the expected value and the variance for the amount that the bank loses on a typical roll.
- Estimate the probability that the bank will lose more than 25 cents in 100 rolls.
- Estimate the probability that the bank will lose exactly 25 cents in 100 rolls.
- Estimate the probability that the bank will lose any money in 100 rolls.
- How many rolls does the bank need to collect to have a 99 percent chance of a net loss?