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 choice
Disagree.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability of the Z score. Multiply by 100.
You should have learned that 68% fall between +1 and -1 deviations of the mean.
Since 20-25 is one standard deviation below the mean, without any calculation I know it is appr 34%
using my favourite stats site
http://davidmlane.com/normal.html
I got .3413 or 34.13%
To find the percentage of commuters who drive between 20-25 minutes to work daily, we can use the concept of z-scores in a normal distribution.
First, let's calculate the z-score for a commute time of 20 minutes. The formula for calculating the z-score is (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
z = (20 - 25) / 5 = -1
Next, let's calculate the z-score for a commute time of 25 minutes (the upper limit of the desired range).
z = (25 - 25) / 5 = 0
Using a standard normal distribution table or a calculator, we can determine the probabilities associated with these z-scores.
The probability corresponding to a z-score of -1 is approximately 0.1587, and the probability corresponding to a z-score of 0 is 0.5.
To find the percentage of commuters who drive between 20-25 minutes, we subtract the lower probability from the upper probability:
0.5 - 0.1587 = 0.3413
Since 0.3413 is approximately 34.13%, the correct answer is therefore C) 34%.
To determine the percent of commuters who drive between 20 - 25 minutes to work daily, we need to calculate the area under the normal curve within this range.
Step 1: Standardize the values
To use the normal distribution, we need to standardize the values by converting them to z-scores. The formula for calculating the z-score is:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation.
For a commute time of 20 minutes, the z-score is:
z1 = (20 - 25) / 5 = -1
For a commute time of 25 minutes, the z-score is:
z2 = (25 - 25) / 5 = 0
Step 2: Find the area under the normal curve
We can use a standard normal distribution table or statistical software to find the area under the curve.
The area to the left of z1 = -1 is 0.1587 (from the standard normal distribution table).
The area to the left of z2 = 0 is 0.5 (from the standard normal distribution table).
So, the area between z1 and z2 is:
Area = 0.5 - 0.1587 = 0.3413
Step 3: Convert to percentage
To get the percentage, we multiply the area by 100.
Percentage = 0.3413 * 100 = 34.13%
Therefore, the percent of commuters who drive between 20 - 25 minutes to work daily is approximately 34%.
The correct answer is C) 34%.