Question

When Aria commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 28 minutes and a standard deviation of 4.5 minutes. Out of the 262 days that Aria commutes to work per year, how many times would her commute be between 32 and 35 minutes, to the nearest whole number ?

Answer 1

To find the number of times that Aria's commute is between 32 and 35 minutes, we need to find the probability that her commute time is between 32 and 35 minutes and then multiply that probability by the total number of commutes per year.

To find the probability that Aria's commute time is between 32 and 35 minutes, we need to find the area under the normal curve between those two values.

We can use the following formula to convert the values 32 and 35 to standard units:

z = (x - mean) / standard deviation

Plugging in the values, we get:

z1 = (32 - 28) / 4.5 = 0.89

z2 = (35 - 28) / 4.5 = 1.56

To find the area under the curve between these two values, we can use a standard normal table or a calculator to find the area between these two values. The result is approximately 0.22.

Multiplying this probability by the total number of commutes per year gives us the number of times that Aria's commute is between 32 and 35 minutes.

So the number of times that Aria's commute is between 32 and 35 minutes is approximately 262 * 0.22 = 57.24, which is about 57 times to the nearest whole number.

Explanation: