Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of...
Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 67 miles per hour, with a standard deviation of 3 miles per hour. Estimate the percent of vehicles whose speeds are between 61 miles per hour and 73 miles per hour. (Assume the data set has a bell-shaped distribution.)
Homework Answers
Solution :
Given that ,
mean = 
=67
standard deviation = 
= 3
P(61< x < 73) = P[(61 - 67) /3 < (x - 
) / 
< (73 - 67 ) /3 )]
= P( -2< Z < 2)
= P(Z <2)+P(Z <-2)
using empirical rule
=95%/2 + 995%/2
=47.5%+47.5%
=95%
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