Points: 0 of 1
A person randomly selects one of six envelopes. Each envelope contains a check that the person gets to keep. Determine the person's expectation if the six envelopes contain checks for $\$ 137$. $\$ 173, \$ 273, \$ 362, \$ 458$, and $\$ 997$.
The expected value is $5 \square$
(Round to the nearest cent as necded.)
Final Answer: The expected value is \(\boxed{400}\).
Step 1 :A person randomly selects one of six envelopes. Each envelope contains a check that the person gets to keep. The six envelopes contain checks for $137, $173, $273, $362, $458, and $997.
Step 2 :The probability of selecting any one envelope is \( \frac{1}{6} \).
Step 3 :The expected value is the sum of the product of each value and its probability.
Step 4 :Calculate the expected value: \( \frac{1}{6} \times 137 + \frac{1}{6} \times 173 + \frac{1}{6} \times 273 + \frac{1}{6} \times 362 + \frac{1}{6} \times 458 + \frac{1}{6} \times 997 \).
Step 5 :The expected value is approximately $400.
Step 6 :Final Answer: The expected value is \(\boxed{400}\).