Question

Question 20 (2.34375 points) According to the U.S. Census Bureau, between 2009-2013, the average commute time was 23.7 minutes one-way. The distribution of one-way commute time is non nally distributed with a standard deviation of 3.5 minutes. Find the 65th percentile for commute time. Round answer to a whole number. A/

Answer 1

Let X denote the one way commute time.

X is normally distributed with mean  $\mu =23.7$ and standard deviation

= 3,5

- Z
where
Z ~ N(0,1)

65th percentile is the value below which 65% of the values of the distribution lies.

Let the 65th percentile be a

P(X <a) = 0.65

$\Rightarrow P(\frac{X-\mu}{\sigma}\leq\frac{a-23.7}{3.5})=0.65$

$\Rightarrow P(Z\leq\frac{a-23.7}{0.35})=0.65$

$\Rightarrow \Phi (\frac{a-23.7}{3.5})=\Phi (0.39)$

$\Rightarrow \frac{a-23.7}{3.5}=0.39$

$\Rightarrow a-23.7=1.365$

$\Rightarrow a=1.365+23.7=25.065\approx 25$

The 65th percentile for commute time is 25

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