Question

undefined When Aiden commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 58 minutes and a standard deviation of 4.5 minutes. What percentage of his commutes will be longer than 61 minutes, to the nearest tenth?

Answer 1

To find the percentage of Aiden's commutes that will be longer than 61 minutes, calculate the z-score for 61 minutes and find the area to the right of that z-score on a standard normal distribution table or calculator. The area to the right of the z-score represents the percentage of commutes longer than 61 minutes. This is approximately 25.1%.

Step-by-step explanation:

To find the percentage of Aiden's commutes that will be longer than 61 minutes, we need to find the area under the normal distribution curve to the right of 61 minutes. We can use the z-score formula to convert the value of 61 minutes to a z-score.

The z-score formula is: z = (x - mean) / standard deviation

Plugging in the values, we get:

z = (61 - 58) / 4.5 = 0.67

We can then use a standard normal distribution table or a calculator to find the area to the right of 0.67. The area to the left of 0.67 is approximately 0.7486, so the area to the right of 0.67 is 1 - 0.7486 = 0.2514.

Therefore, approximately 25.1% of Aiden's commutes will be longer than 61 minutes.