Respuesta :
Answer:
54.03% probability that a randomly selected road has between 128 and 136 potholes per 10 miles.
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 have that:
[tex]\mu = 130, \sigma = 5[/tex]
Find the probability that a randomly selected road has between 128 and 136 potholes per 10 miles.
This probability is the pvalue of Z when X = 136 subtracted by the pvalue of Z when X = 128. So
X = 136
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{136 - 130}{5}[/tex]
[tex]Z = 1.2[/tex]
[tex]Z = 1.2[/tex] has a pvalue of 0.8849.
X = 128
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{128 - 130}{5}[/tex]
[tex]Z = -0.4[/tex]
[tex]Z = -0.4[/tex] has a pvalue of 0.3446.
0.8849 - 0.3446 = 0.5403
54.03% probability that a randomly selected road has between 128 and 136 potholes per 10 miles.
