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?

61.25 mph

Step-by-step 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