Question

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 4.5 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

Using the normal distribution, it is found that the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot is of 3.7 minutes.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given as follows:

$\mu = 4.5, \sigma = 1$

The cut-off time is the 100 - 75.8 = 24.2th percentile, which is X when Z = -0.7, hence:

$Z = \frac{X - \mu}{\sigma}$

$-0.7 = \frac{X - 4.5}{1}$

X - 4.5 = -0.7

X = 3.7.

More can be learned about the normal distribution at brainly.com/question/4079902

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