Question

A traffic survey revealed that the speeds of vehicles along

adangerous stretch of interstate follow a normal distribution
withmean 50 mph and standard deviation 8 mph. What speed should
beposted so that only 8% of all drivers monitored are guilty
ofspeeding?

Answer 1

61.25 mph

Explanation:

Data provided in the question:

Mean of the normal distribution = 50 mph

Standard deviation = 8 mph

Now,

let X be the speed limit

z score for the speed X = [ X - Mean ] ÷ Standard deviation

= [ X - 50 ] ÷ 8

According to the question

P (z > {[ X - 50 ] ÷ 8} ) = 8% = 0.08

also,

0.08 = P( z > 1.406 ) [From standard z table ]

therefore,

[ X - 50 ] ÷ 8} = 1.406

or

X - 50 = 11.248

or

X = 50 + 11.248

or

X = 61.248 ≈ 61.25 mph