A mathematician is analyzing an email message. Out of the first 100 characters, the letter e appears 13 times. The email message is 1,100 characters in length. Based on the information, how many of the characters should be a letter e?

Question

A.
85

B.
118

C.
143

D.
113

Answer 1

To determine the expected number of the letter 'e' in the entire email message based on the observed frequency in the first 100 characters, we can first calculate the frequency of 'e' in those characters.

In the first 100 characters, the letter 'e' appears 13 times. This gives us a frequency of:

\[ \text{Frequency of 'e'} = \frac{13}{100} = 0.13 \]

Next, we apply this frequency to the total length of the email, which is 1,100 characters. We calculate the expected number of 'e's in the full email:

\[ \text{Expected number of 'e's} = 1,100 \times 0.13 = 143 \]

Thus, the expected number of characters that should be the letter 'e' in the entire email message is 143.

The correct answer is:

C. 143