A typist at a constant speed of 65 words per minute makes a mistake in any particular word with probability 0.06, independently from word to word. Each incorrect word must be corrected, a task which takes 14 seconds per word. Find the mean of the time (in seconds, round-off to an integer) it takes to finish a 675-word passage.
To find the mean time it takes to finish a 675-word passage, we need to calculate the time it takes to type and correct each word.
Let's break down the time for each word:
1. Typing time: Since the typist types at a constant speed of 65 words per minute, the typing time for each word is 60 seconds divided by 65 words, approximately 0.923 seconds per word.
2. Correction time: Each incorrect word must be corrected, and it takes 14 seconds per word to do so.
Now, let's calculate the mean time:
First, we need to calculate the number of incorrect words in a 675-word passage. The probability of making a mistake in any particular word is given as 0.06.
The number of incorrect words can be calculated using the formula:
Number of incorrect words = Total words * Probability of error
Number of incorrect words = 675 * 0.06 = 40.5
Since the number of words must be a whole number, we round 40.5 to the nearest whole number, which is 41.
Now, let's calculate the mean time:
Typing time:
Typing time for each correct word = 0.923 seconds/word
Total typing time for correct words = 0.923 seconds/word * (675 - 41) words
Correction time:
Correction time for each incorrect word = 14 seconds/word
Total correction time for incorrect words = 14 seconds/word * 41 words
Mean time to finish the passage = Total typing time + Total correction time
Mean time = (0.923 * (675 - 41)) + (14 * 41) seconds