Question

Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 68 miles per​ hour, with a standard deviation 3 of miles per hour. Estimate the percent of vehicles whose speeds are between 59 miles per hour and miles per hour.​ (Assume the data set has a​ bell-shaped distribution.)

Answer 1

The question is an illustration of probabilities from z score.

The percentage of vehicles whose speeds are between 59 miles per hour and 77 miles per hour is 99.73%

The given parameters are:

$\mu = 68$ -- the mean

$\sigma = 3$ --- the standard deviation

The percent of vehicles between 59 and 77 miles per hour is represented as:

$x_1 = 59$

$x_2 = 77$

So, the probability is represented as:

$P(59 < x < 77) = P(z_1 < z < z_2)$

Calculate the z values using:

$z = \frac{x - \mu}{\sigma}$

When $x_1 = 59$

$z_1 = \frac{59 - 68}{3} = -3$

When $x_2 = 77$

$z_2 = \frac{77 - 68}{3} = 3$

So, we have:

$P(59 < x < 77) = P(z_1 < z < z_2)$

$P(59 < x < 77) = P(-3 < z < 3)$

Using empirical rule:

$P(-3$ --- from z table of probabilities

So, we have:

$P(59$

Represent as percentage

$P(59$

$P(59$

Hence, the percentage of vehicles whose speeds are between 59 miles per hour and 77 miles per hour is 99.73%

Read more about z score probabilities at:

brainly.com/question/16464000

Answer 2

About 99.7% of vehicles whose speeds are between 59 miles per hour and 77 miles per hour.

Empirical rule states that for a normal distribution, 68% lie within one standard deviations, 95% lie within two standard deviations, and 99.7% lie within three standard deviations of the mean.

Given that mean (μ) = 68 miles per hour, standard deviation (σ) = 3 miles per hour.

68% lie within one standard deviation = (μ ± σ) = (68 ± 3) = (65, 71).

Hence 68% of the vehicle speed is between 65 miles per hour and 71 miles per hour.

95% lie within two standard deviation = (μ ± 2σ) = (68 ± 2*3) = (62, 74).

Hence 95% of the vehicle speed is between 62 miles per hour and 74 miles per hour.

99.7% lie within three standard deviation = (μ ± 3σ) = (68 ± 3*3) = (59, 77).

Hence 99.7% of the vehicle speed is between 59 miles per hour and 77 miles per hour.

Find out more at: brainly.com/question/14468516