Question

Avoiding an accident when driving can depend on reaction time. That time, measured in seconds from the moment the driver see danger until they step on the brake pedal, can be described by the Normal model with a mean of 1.5 seconds and a standard deviation of 0.18 seconds.

Note that this scenario is talking about a population distribution. There is no discussion of a sample or sample size. Therefore, you do not need to adjust the standard deviation that is given before using the normalcdf and invNorm commands.



a) What percent of drivers have a reaction time greater than 1.8 seconds?

Give the command and values you used as a way of showing your work:

Give your final answer rounded to 2 decimal places:



b) Describe the reaction time of the slowest 10% of all drivers? (Hint: The slower a person reacts, the higher their reaction time so this is looking at the right tail of the distribution)

Give the command and values you used as a way of showing your work:

Give your final answer rounded to 2 decimal places:

Answer 1

Using the normal distribution, it is found that:

a) 4.75% of drivers have a reaction time greater than 1.8 seconds.

b) The reaction time is of at least 1.73 seconds.

Normal Probability Distribution

In a normal distribution with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

• It measures how many standard deviations the measure is from the mean.

• After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem, the mean and the standard deviation are given by, respectively:

$\mu = 1.5, \sigma = 0.18$

Item a:

The proportion is one subtracted by the p-value of Z when X = 1.8, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1.8 - 1.5}{0.18}$

$Z = 1.67$

$Z = 1.67$ has a p-value of 0.9525.

1 - 0.9525 = 0.0475 = 4.75%.

4.75% of drivers have a reaction time greater than 1.8 seconds.

Item b:

The reaction time is of at least X seconds, in which X is the 90th percentile, that is, X when Z = 1.28, hence:

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{X - 1.5}{0.18}$

$X - 1.5 = 1.28(0.18)$

$X = 1.73$

The reaction time is of at least 1.73 seconds.

More can be learned about the normal distribution at https://brainly.com/question/24663213