Chapter 6: Q. 37 (page 384)

The time $X$ it takes Hattan to drive to work on a randomly selected day follows a distribution that is approximately Normal with mean $15$ minutes and standard deviation $6.5$ minutes. Once he parks his car in his reserved space, it takes $5$ more minutes for him to walk to his office. Let $T =$ the total time it takes Hattan to reach his office on a randomly selected day, so $T = X + 5$ . Describe the shape, center, and variability of the probability distribution of $T$ .

Expert verified

$T$ is a normal distribution with a mean of $20$ and a standard deviation of $6.5$ minutes.

Step by step solution

Given:

The time taken by Hattan to drive to work is : $X$

Time taken is Normal with mean : $15$ minutes

Standard deviation : $6.5$ minutes

It takes for him to walk to his office : $5$ minutes

$T =$ the total time it takes Hattan to reach his office

$\Rightarrow T = X + 5$

Shape :

T

is a normal distribution function since adding the constant to every data value has no effect on the shape of the distribution.

Center:

When the constant is added to each data value, the center of the distribution is also enlarged, making $T$ a normal distribution function.

$μ_{T} = μ_{X} + 5 = 15 + 5 = 20$

Spread:

When you add the constant to every data value, the spread of the distribution does not change; it stays the same.

$σ_{T} = σ_{X} = 6.5$

Unlock Step-by-Step Solutions & Ace Your Exams!

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.