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

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belgrad belgrad · Answer 1 · 2021-02-07T03:00:32+01:00

Answer:

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

P(62≤X≤70) = 68.76

Step-by-step 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

[tex]Z = \frac{x^{-}-mean }{S.D} = \frac{62-66}{4} =-1[/tex]

let x=70

[tex]Z = \frac{70-66 }{4} = \frac{70-66}{4} =1[/tex]

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