Question

Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 64 miles per hour, with a standard deviation of 5 miles per hour. Estimate the percent of vehicles whose speeds are between 59 miles per hour and 69 miles per hour. (Assume the data set has a bell-shaped distribution.) Approximately % of vehicles travel between 59 miles per hour and 69 miles per hour.

Answer 1

Solution :

Given that ,

mean = $\mu$ = 64

standard deviation = $\sigma$ = 5

P(59< x < 69) = P[(59 - 64) / 5< (x - $\mu$ ) / $\sigma$ < (69 - 64) /5 )]

= P( -1< Z <1 )

= P(Z < 1) +P(Z < -1)

using empirical rule

=68%/2 +68%/2

=34%+34%

=68%