Mathematics: The distance around a neighborhood is 4 miles. when clicking it with an odometer, the distance was 3.8 miles. what is the percent error?

The distance around a neighborhood is 4 miles. when

emilyscroggins794

09.01.2023

The mean time for commute is 22.46 minutes.

Step-by-step explanation:

We are given the following information in the question:

Standard Deviation, σ = 6.3 minutes

We are given that the distribution of commute times in a large city is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(more than 20 minutes to commute one-way) = 65.20% = 0.6520

P(X > 20) = 0.6520

$P( x 20) = P( z \displaystyle\frac{20 - \mu}{6.3}) = 0.6520$

$= 1 - P(z \leq \displaystyle\frac{20 - \mu}{6.3}) = 0.6520$

$P(z \leq \displaystyle\frac{20 - \mu}{6.3}) =1-0.6520=0.348$

Calculation the value from standard normal z table, we have,

$P(z \leq -0.391) =0.348$

$\displaystyle\frac{20 - \mu}{6.3} = -0.391$

Solving, we get,

$\mu = 22.46\text{ minutes}$

The mean time for commute is 22.46 minutes.

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