Question

The mean speed of vehicles along a stretch of highway is 56 mph with a standard deviation of 4 mph. You
measure the speed of three cars traveling along this stretch of highways as 62 mph, 47 mph, and 56 mph. Find the
z-score that corresponds to each speed.

Answer 1

The corresponding z score for speed of 62 mph, 47 mph, and 56 mph is 1.5, -2.25 and 0 respectively.

Z score

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

$z=\frac{x-\mu}{\sigma }$

Where x is raw score, μ is mean, σ is standard deviation

Given that:

σ = 4, μ = 56, hence

for x = 62:

$z=\frac{62-56}{4 } =1.5$

for x = 47:

$z=\frac{47-56}{4 } =-2.25$

for x = 56:

$z=\frac{56-56}{4 } =0$

The corresponding z score for speed of 62 mph, 47 mph, and 56 mph is 1.5, -2.25 and 0 respectively.

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