Final answer:
The typing speed at the 92nd percentile for a normal distribution with a mean of 43 words per minute and a standard deviation of 12 words per minute is approximately 59.92 words per minute.
Step-by-step explanation:
To find the typing speed that corresponds to the 92nd percentile given a normal distribution with a mean of 43 words per minute and a standard deviation of 12 words per minute, we can use the z-score formula. First, we determine the z-score that corresponds to the 92nd percentile. In standard normal distribution tables, or using software or a calculator that provides this functionality, we see that a z-score of approximately 1.41 corresponds to the 92nd percentile. Next, we apply the z-score formula to find the specific typing speed.
The formula is:
X = μ + (z × σ)
where X is the value for the percentile, μ is the mean, z is the z-score, and σ is the standard deviation.
Plugging in the values:
X = 43 + (1.41 × 12)
= 43 + 16.92
= 59.92
Thus, the typing speed at the 92nd percentile is approximately 59.92 words per minute.