Final answer:
The probability that the mean speed of 25 randomly chosen cars is less than 70 miles/hour is approximately 0.0032 or 0.32%, calculated using the standard error of the mean and the z-score in a standard normal distribution.
Step-by-step explanation:
The student is asking for the probability that the mean speed of 25 randomly chosen cars on the Interstate 5 Freeway in California is less than 70 miles/hour, given that the mean speed is 72.6 miles/hour and the standard deviation is 4.78 miles/hour. Since the distribution of speeds is nearly normal, we can use the Central Limit Theorem to find this probability.
To solve this problem, we first calculate the standard error of the mean (SEM), which is the standard deviation divided by the square root of the sample size. In this case, SEM = 4.78 / √25 = 0.956. Next, we calculate the z-score for 70 miles/hour, which is (70 - 72.6) / 0.956 = -2.72.
Finally, we look up the z-score in a standard normal distribution table or use a statistical software to find the probability associated with a z-score of -2.72. The probability that the mean speed of 25 cars is less than 70 miles/hour is the area under the normal curve to the left of -2.72, which is approximately 0.0032 or 0.32%.