Question

After recording the maximum distance possible when driving a new electric car this study showed the distance is follow the normal distribution the mean distance is 134 miles and the standard deviation is 4.8 miles find the probability that in a random test from the car will travel maximum distance between 125 and 135 miles

Answer 1

To find the probability that the car will travel a maximum distance between 125 and 135 miles, we need to calculate the z-scores for these distances and find the corresponding probabilities using a standard normal distribution table or calculator.

Step-by-step explanation:

To find the probability that the car will travel a maximum distance between 125 and 135 miles, we need to calculate the z-scores for these distances using the formula: z = (x - mean) / standard deviation.

For 125 miles: z = (125 - 134) / 4.8 = -1.875.

For 135 miles: z = (135 - 134) / 4.8 = 0.208.

Next, we need to find the corresponding probabilities for these z-scores using a standard normal distribution table or calculator. The probability of a z-score less than -1.875 is approximately 0.0301, and the probability of a z-score less than 0.208 is approximately 0.5829.

To find the probability between 125 and 135 miles, we subtract the probability of a z-score less than 125 from the probability of a z-score less than 135: 0.5829 - 0.0301 = 0.5528.

Therefore, the probability that the car will travel a maximum distance between 125 and 135 miles is approximately 0.5528 or 55.28%.

Answer 2

the answer is 0.5531 (✿◠‿◠)