Final answer:
To find the probability that the reaction time is between 6 and 8 minutes, we can use the cumulative distribution function (CDF) and the Z-score formula.
Step-by-step explanation:
The probability that the reaction time is between 6 and 8 minutes can be calculated using the cumulative distribution function (CDF) of the reaction time. Let's denote the variable X as the reaction time. Assuming X follows a normal distribution with mean µ and standard deviation σ, we can use the following formula:
P(6 < X < 8) = P(X < 8) - P(X < 6)
Next, we can use the Z-score formula to standardize the values of 6 and 8:
Z1 = (6 - µ) / σ
Z2 = (8 - µ) / σ
Finally, we can use the standard normal distribution table or a calculator to find the probabilities associated with the Z-scores Z1 and Z2 and calculate P(6 < X < 8).