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.)

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 \(\boxed{400}\).