Question

1.) The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This distribution has a mean of 54 and a standard deviation of 8. Using the empirical rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 38 and 62?

2.) The physical plant at the main campus of a large state university receives daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 60 and a standard deviation of 8. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 60 and 68?

Answer 1

SOLUTION:

Solution :

Given that ,

mean = =54

standard deviation = = 8

P(38< x < 62) = P[(38 - 54) /8 < (x - ) / < (62 - 54 ) /8 )]

= P( -2< Z < 1)

= P(Z <1)+P(Z <-2 )

using empirical rule

=68%/2 + 95%/2

=34%+47.5%

=81.50%

2)

Solution :

Given that ,

mean = =60

standard deviation = = 8

P(60< x < 68) = P[(60 - 60) /8 < (x - ) / < (68 - 60) /8)]

= P( 0< Z < 1)

= P(Z <1)+P(Z <0 )

using empirical rule

=68%/2 + 0%/2

=34%+0%

=34%