Question

A car's speed limit is 20 mph. The mean speed of 100 cars is 21.96 mph, with a standard deviation of 3.28 mph. One car's z-score was +1.5. How fast was that car going?

a) 19.45 mph
b) 24.94 mph
c) 22.72 mph
d) 25.18 mph

Answer 1

Step-by-step explanation:

Z-score of + 1.5 means the car is going + 1.5 times the Standard Deviation ABOVE the limit ....

1.5 * 3.28 = 4.92 mph above the limit

20 + 4.92 = 24.92 mph

Answer 2

After applying the z-score formula to the provided mean and standard deviation, the calculated speed of the car is 26.88 mph. However, this does not match any of the options given, indicating a potential error in the question or answer choices. The closest provided option is 24.94 mph.

Step-by-step explanation:

The question is asking to determine the speed of a car based on its z-score in a data set with a given mean and standard deviation. You can find the speed of the car by using the formula that relates a z-score in a normally distributed set of data to the actual value:

Speed = mean + (z-score × standard deviation)

In the situation provided:

• Mean speed = 21.96 mph
• Standard deviation = 3.28 mph
• Z-score of the car = +1.5

Now, using the formula:

Speed = 21.96 mph + (1.5 × 3.28 mph)

Speed = 21.96 mph + 4.92 mph

Speed = 26.88 mph

Based on the provided options, none of them match the calculated speed. There might be a typo in the question, and the closest speed to the calculated one is b) 24.94 mph.