speeding ND

[summertigger]

A traffic survey revealed that the speeds of vehicles along a dangerous stretch of interstate follow a normal distribution with mean 50mph and standard deviation 8 mph. What speed limit should be posted so that only 8% of all drivers monitored are guilty of speeding?

.5000 - .08 = .42
=.4192 = 1.4

=50 + (-1.4)(2)
=50 - 2.8
=47.2

47mph

Right?

[JohnM]

The z score that divides the lower 92% and upper 8% of the normal curve is 1.405, so you got that part right.

You need to set the speed limit higher than the average speed, otherwise you'll get a lot more than 8% will get caught speeding.

z = (x - mu)/s

1.405 = (x - 50)/8

Solve for x.

[summertigger]

=50 + (1.4)(8)
=50 + 11.2
=61.2

61 mph