Question

provide an appropriate response. the length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 7.0 minutes and a standard deviation of 1 minute. find the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot.

Answer 1

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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