the number of potholes in any given 1 - mile stretch of freeway pavement in pennsylvania has a bell - shaped distribution. this distribution has a mean of 49 and a standard deviation of 10. using the empirical rule (as presented in the book), what is the approximate percentage of 1 - mile long roadways with potholes numbering between 29 and 59?
(round percent number to 2 decimal places.)
do not enter the percent symbol.
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Accepted Answer

# Explanation:
## Step1: Calculate the number of standard deviations from the mean
For $x = 29$, $z=\frac{29 - 49}{10}=\frac{- 20}{10}=-2$
For $x = 59$, $z=\frac{59 - 49}{10}=\frac{10}{10}=1$

## Step2: Apply the empirical rule
The empirical rule states that for a bell - shaped (normal) distribution:
- Approximately $68\%$ of the data lies within $z=-1$ and $z = 1$
- Approximately $95\%$ of the data lies within $z=-2$ and $z = 2$

The proportion of data between $z=-2$ and $z = 1$ is $\frac{95\%+68\%}{2}$ (using the symmetry of the normal distribution).
$$P(-2<Z<1)=\frac{95 + 68}{2}\%=\frac{163}{2}\% = 81.5\%$$

# Answer:
81.50

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the number of standard deviations from the mean

Step2: Apply the empirical rule

Answer: