Question

A driver’s reaction time to brake lights on a decelerating vehicle can be modeled with a normal distribution where the mean is 1.25 seconds and the standard deviation is 0.4 seconds.

(a) Find the z-score for a reaction time of 1.00 seconds. Round to 2 decimal places.

(b) Find the z-score for a reaction time of 1.75 seconds. Round to 2 decimal places.

(c) Using z-scores and your calculator: What is the probability that reaction time is between 1.00 and 1.75 seconds? Write the calculator formula you used to answer this question, along with the parameters. (We did this every time in class)

(d) Without using z-scores (using the original parameters) and your calculator: What is the probability that reaction time is between 1.00 and 1.75 seconds? Write the calculator formula you used to answer this question, along with the parameters. (We did this every time in class)

(e) About 68% of the reaction times lie between what two values (use the original parameters)?

Answer 1

We would be looking at the first 4 parts here as:

a) The z score for the reaction time of 1 second is computed here as:

Therefore -0.625 is the required z score here.

b) The z score for the reaction time of 1.75 second is computed here as:

Therefore 1.25 is the required z score here.

c) To compute this on calculator, we have been asked the steps. The probability here is computed as:

Press “2nd” “DISTR” → normalcdf(a, b, μ, σ) tells you the area of the between a and b for the given mean μ, and standard deviation σ.

Using the Z scores, the probability here is computed as:

= normalcdf(-0.625 , 1.25, 0, 1)

The probability output here is given to be: 0.628

Therefore 0.628 is the required probability here.

d) Now using the raw x values, we compute the probability in calculator here as:

= normalcdf(1, 1.75, 1.25, 0.4)

The probability output here is given to be: 0.628

Therefore 0.628 is the required probability here.