Final answer:
To find the mean number of times 'n' appears on a page, multiply the number of characters (2300) by the frequency (6.65%), resulting in approximately 153 'n's per page. The standard deviation is found using the square root of 2300 multiplied by the probability of 'n' and its complement, resulting in approximately 12.197.
Step-by-step explanation:
The student is asking a question related to the use of probability and statistics to analyze frequencies of letters in English text, specifically focusing on the letter 'n'. Given that 'n' appears in standard English text at a rate of 6.65%, and considering a typical page to consist of 2300 characters, we wish to find the mean and standard deviation for the occurrence of 'n' on such a page. Using the binomial distribution assumptions, where n is the number of trials (characters on a page) and p is the probability of success (the letter 'n' appearing), the mean (expected value) is calculated as:
Mean (μ) = n * p
Substitute the given values:
μ = 2300 * 6.65% ≈ 153.045
This means on average, we expect to see about 153 instances of the letter 'n' on a page. To find the standard deviation (σ), we use the formula for the binomial distribution:
Standard Deviation (σ) = √(n * p * (1 - p))
Substitute the given values:
σ = √(2300 * 0.0665 * (1 - 0.0665)) ≈ √(153.045 * 0.9335) ≈ 12.197
Thus, the standard deviation is approximately 12.197, indicating the variability we might expect in the count of 'n's on a page.