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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.

Respuesta :

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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • 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:

[tex]\mu = 4.5, \sigma = 1[/tex]

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.7 = \frac{X - 4.5}{1}[/tex]

X - 4.5 = -0.7

X = 3.7.

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

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