Respuesta :
The probability that a randomly selected college student will find a parking spot in the library parking lot in less than 5.0 minutes, using the normal distribution, is of:
0.3085 = 30.85%.
How to obtain probabilities using the normal distribution?
The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.
- Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.
The mean and the standard deviation for the times are given as follows:
[tex]\mu = 5.5, \sigma = 1[/tex]
The probability of taking less than 5 minutes is the p-value of Z when X = 5, hence:
Z = (5 - 5.5)/1
Z = -0.5.
Z = -0.5 has a p-value of 0.3085.
Hence the probability is of:
0.3085 = 30.85%.
More can be learned about the normal distribution at https://brainly.com/question/25800303
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