By the distribution,6.3 minutes is the time limit that 75.8% of college students go over when looking for a parking space in the library parking lot.
Given that,
Finding a parking spot in the library parking lot takes college students an average of 7.0 minutes, with a standard deviation of 1 minute, according to a normal distribution.
Find the window of opportunity that 75.8% of college students miss when looking for a place in the library parking lot.
The following formula calculates the z-score of a measure X of a normally distributed variable with mean μ and standard deviationσ:
Z=(X-μ)/σ
The z-score calculates how far the measure deviates from the mean by standard deviation.
The p-value for this z-score, which is the percentile of X, can be obtained by looking at the z-score table.
The cut-off time is the 100th percentile minus 75.8th percentile, or X, for Z = -0.7, so:
Z=(X-μ)/σ
-0.7=(X-7)/1
-0.7=X-7
X=-0.7+7
X=6.3
Therefore, 6.3 minutes is the time limit that 75.8% of college students go over when looking for a parking space in the library parking lot.
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radians.