Respuesta :
Answer:
56.75% probability that a mechanic can complete 16 oil changes in an eight-hour day
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 = 29.5, \sigma = 3[/tex]
What is the probability that a mechanic can complete 16 oil changes in an eight-hour day
16 oil changes in an eight hour days is 16/8 = 2 oil changes per hour, that is, one each 60/2 = 30 minutes.
So this probability is the pvalue of Z when X = 30. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 29.5}{3}[/tex]
[tex]Z = 0.17[/tex]
[tex]Z = 0.17[/tex] has a pvalue of 0.5675
56.75% probability that a mechanic can complete 16 oil changes in an eight-hour day
