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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.

Short Answer

Expert verified

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

Step by step solution

01

Given information

Given:

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

Time taken is Normal with mean : 15minutes

Standard deviation : 6.5minutes

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

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

鈬�T=X+5

02

Describing the shape, center, and variability of the probability distribution of T

Shape :

Tis 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 Ta normal distribution function.

渭T=渭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.

蟽T=蟽X=6.5

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