Respuesta :
Answer:
A time of 3.65 minutes is exceeded by approximately 75% of the college students when trying to find a parking spot in the main parking lot
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 5, \sigma = 2[/tex]
What time is exceeded by approximately 75% of the college students when trying to find a parking spot in the main parking lot?
This is 100-75 = 25th percentile, which is X when Z has a pvalue of 0.25. So it is X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 5}{2}[/tex]
[tex]X - 5 = -0.675*2[/tex]
[tex]X = 3.65[/tex]
A time of 3.65 minutes is exceeded by approximately 75% of the college students when trying to find a parking spot in the main parking lot
