Question

When avani commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 32 minutes and a standard deviation of 3.5 minutes. what percentage of her commutes will be between 31 and 34 minutes, to the nearest tenth?

Answer 1

To find the percentage of Avani's commutes that will be between 31 and 34 minutes, we calculate the z-scores for these values and find the area under the normal curve.

Step-by-step explanation:

To find the percentage of Avani's commutes that will be between 31 and 34 minutes, we need to calculate the z-scores for these values and then find the area under the normal curve between the z-scores.

First, we calculate the z-score for 31 minutes using the formula: z = (x - μ) / σ. Plugging in the values, we get: z = (31 - 32) / 3.5 = -0.2857. Similarly, the z-score for 34 minutes is 0.8571.

Next, we use a standard normal distribution table or a calculator to find the area under the curve between these z-scores. The area between -0.2857 and 0.8571 is approximately 0.3471.

Therefore, approximately 34.7% of Avani's commutes will be between 31 and 34 minutes.

Answer 2

To find the percentage of Avani's commutes between 31 and 34 minutes, calculate the z-scores and find the corresponding area under the normal curve.

Step-by-step explanation:

To find the percentage of Avani's commutes that will be between 31 and 34 minutes, we need to calculate the z-scores for both times and find the corresponding area under the normal distribution curve.

First, we calculate the z-score for 31 minutes using the formula: z = (x - mean) / standard deviation. Then, we calculate the z-score for 34 minutes. Next, we use a z-score table or a calculator to find the area under the normal curve between these two z-scores. Finally, we multiply the area by 100 to get the percentage.

Let's do the calculations:

z-score for 31 minutes: z = (31 - 32) / 3.5 = -0.2857

z-score for 34 minutes: z = (34 - 32) / 3.5 = 0.5714

Using a z-score table or a calculator, we find that the area between -0.2857 and 0.5714 is approximately 0.3094. Multiplying this by 100, we get 30.94%. Therefore, approximately 30.9% of Avani's commutes will be between 31 and 34 minutes.