Question

The reaction time of a driver to visual stimulus is normally distributed with a mean of 0.4 seconds and a standard deviation of 0.05 seconds. What is the probability that a driver's reaction time is less than 0.35 seconds?

Answer 1

To find the probability of a driver's reaction time being less than 0.35 seconds, we calculate the Z-score and refer to a standard normal distribution table. The Z-score for 0.35 seconds is -1, which corresponds to a probability of about 15.87%.

Step-by-step explanation:

The probability that a driver's reaction time is less than 0.35 seconds can be found by using the Z-score formula:

Z = (X - μ) / σ

Where X is the value of interest (0.35 seconds), μ is the mean reaction time (0.4 seconds), and σ is the standard deviation (0.05 seconds).

Calculating the Z-score:

Z = (0.35 - 0.4) / 0.05 = -1

The Z-score of -1 corresponds to a probability of 15.87% on a standard normal distribution table. This is the probability that a driver's reaction time is less than 0.35 seconds.