Respuesta :
Answer:
The standard deviation of the speeds of cars travelling on California freeway is 6.0088 miles per hour.
Step-by-step explanation:
Problems of normally distributed samples can be 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]
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 This p-value is the probability that the value of the measure is greater than X.
In this problem, we have that:
Suppose that the speeds of cars travelling on California freeways are normally distributed with a mean of 61 miles/hour. This means that [tex]\mu = 61[/tex].
The highway patrol's policy is to issue tickets for cars with speeds exceeding 75 miles/hour. The records show that exactly 1% of the speeds exceed this limit. This means that the pvalue of Z when [tex]X = 75[/tex] is 0.99. This is [tex]Z = 2.33[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.33 = \frac{75 - 61}{\sigma}[/tex]
[tex]2.33\sigma = 14[/tex]
[tex]\sigma = \frac{14}{2.33}[/tex]
[tex]\sigma = 6.0088[/tex]
The standard deviation of the speeds of cars travelling on California freeway is 6.0088 miles per hour.
