Question

Use the empirical rule. the mean speed of a sample of vehicles along a stretch of highway is 66 miles per​ hour, with a standard deviation of 4 miles per hour. estimate the percent of vehicles whose speeds are between 62 miles per hour and 70 miles per hour.​ (assume the data set has a​ bell-shaped distribution.)

Answer: 99.7

Answer 1

The percentage of that vehicles whose speeds are between 62 miles per hour and 70 miles per hour

P(62≤X≤70) = 68.76

Explanation:

Step(i):-

Given that the mean of the Population = 66miles per hour

Given that the standard deviation of the Population = 4 miles per hour

Let 'X' be the random variable in normal distribution

Let x= 62

`Z = (x^(-)-mean )/(S.D) = (62-66)/(4) =-1`

let x=70

`Z = (70-66 )/(4) = (70-66)/(4) =1`

Step(ii):-

The probability that vehicles whose speeds are between 62 miles per hour and 70 miles per hour

P(62≤X≤70) = P(-1≤Z≤1)

= P(z≤1) -P(Z≤-1)

= P(Z≤1)+P(Z≤1)

= 2×P(Z≤1)

= 2×0.3438

= 0.6876

The percentage of that vehicles whose speeds are between 62 miles per hour and 70 miles per hour

P(62≤X≤70) = 68.76