Final answer:
Approximately 13 out of 300 cars are expected to be traveling slower than 45 mph based on the normal distribution with a mean of 62 mph and standard deviation of 10 mph, none of the provided answer choices are correct.
Step-by-step explanation:
To determine how many cars will be traveling slower than 45 mph, we need to use the properties of the normal distribution. The problem states that the mean speed is 62 mph, and the standard deviation is 10 mph. We can calculate the z-score for a speed of 45 mph.
Z = (X - μ) / σ = (45 - 62) / 10 = -1.7
Next, we use a z-table or standard normal distribution table to find the probability that a car is traveling slower than 45 mph, which corresponds to a z-score of -1.7. This probability is roughly 0.0446.
We then multiply this probability by the total number of cars:
Number of cars traveling slower than 45 mph = Probability * Total number of cars = 0.0446 * 300 ≈ 13
Since 13 is not among the provided answer choices, we may consider checking the calculation for any potential errors or confirm that the available options do not match the calculated result and investigate accordingly.