In a distribution of 400 response times with a mean of 7 minutes and a standard deviation of 2 minutes, the maximum number of response times greater than 13 minutes would be about:
A. 40
B. 100
C. 75
D. 90
According to
http://davidmlane.com/hyperstat/z_table.html
the probability of a time greater than 13 minutes is .00135
None of your choices result from that probability.
Z = (x - μ)/SD
Z = (13-7)/2 = 6/2 = 3
Look up this Z in a table in the back of your statistics text covering areas under the normal distribution for the smallest area. Multiply this value by 400.
Unfortunately, that does not fit any of your choices. Do you have any typos?
No. No typos. That's how its written on the packet I am doing. Thank You so much for your help though, I guess my teacher might've made a typo...
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To find the maximum number of response times greater than 13 minutes in a distribution with a given mean and standard deviation, we can use the concept of the normal distribution.
First, we need to standardize the value of 13 minutes using the formula for standardizing a value:
z = (x - μ) / σ
Where:
z is the standardized value (z-score)
x is the value we want to convert to a z-score (in this case, 13 minutes)
μ is the mean of the distribution (7 minutes)
σ is the standard deviation of the distribution (2 minutes)
Calculating the z-score for 13 minutes:
z = (13 - 7) / 2
z = 6 / 2
z = 3
Now, we can use a standard normal distribution table or a statistical calculator to find the proportion of values that have a z-score greater than 3. This proportion represents the percentage of response times greater than 13 minutes.
Using a standard normal distribution table, we can find that the proportion of values with a z-score greater than 3 is approximately 0.0013. This means that about 0.13% of the response times would be greater than 13 minutes.
To calculate the actual number of response times greater than 13 minutes out of a distribution of 400 response times, we multiply the proportion by the total number of response times:
Number = Proportion * Total
Number = 0.0013 * 400
Number = 0.52
Therefore, the maximum number of response times greater than 13 minutes would be approximately 0.52. Since the number of response times must be a whole number, we round this number to the nearest whole number, which is 1.
However, none of the answer choices (A. 40, B. 100, C. 75, D. 90) are close to 1. It seems there might be an error in the question or answer choices as they do not align with the calculations and the concept of the normal distribution.