The commute times during rush hour traffic on a local interstate have a mean of 25 minutes and a standard deviation of 5 minutes. Repeated studies of this section of interstate are considered normally distributed. What percent of commuters drive between 20 - 25 minutes to work daily?
A) 16%
B) 32%
C) 34%
D) 50%
My answer choice is C
What school subject is this?
This is Algebra 2
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To find the percentage of commuters who drive between 20-25 minutes to work daily, we can use the concept of standard deviations.
First, we need to standardize the values of 20 and 25 minutes using the formula for z-score:
z = (x - μ) / σ
where x is the value we are interested in (in this case, 20 and 25 minutes), μ is the mean commute time (25 minutes), and σ is the standard deviation (5 minutes).
For 20 minutes:
z = (20 - 25) / 5 = -1
For 25 minutes:
z = (25 - 25) / 5 = 0
Now, we need to find the area under the normal distribution curve between -1 and 0. We can use a Z-table or a calculator to find this area.
Looking up the z-scores in the Z-table, we find that the area to the left of -1 is approximately 0.1587 and the area to the left of 0 is approximately 0.5.
To find the area between -1 and 0, we subtract the area to the left of -1 from the area to the left of 0:
0.5 - 0.1587 ≈ 0.3413
So approximately 34.13% of commuters drive between 20-25 minutes to work daily.
Therefore, the correct answer is C) 34%.