Answer: 0.0026
Step-by-step explanation:
Given: Mean : [tex]\mu=8.4\text{ hours}[/tex]
Standard Deviation : [tex]\sigma = 1.8\text{ hours}[/tex]
Sample size : [tex]n=40[/tex]
Formula to calculate z-score :-
[tex]z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
For X=7.6 hours.
[tex]z=\dfrac{7.6-8.4}{\dfrac{1.8}{\sqrt{40}}}=-2.81091347571\approx-2.8[/tex]
[tex]P(X<7.6)=P(Z<-2.8)=0.0025551\approx0.0026[/tex]
Hence, the probability that their mean rebuild time is less than 7.6 hours = 0.0026
The probability that their mean rebuild time is less than 7.6 hours is 0.0026
A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 7.6 hours.
The Chevrolet Cavalier is the line of small cars produced for the model years 1982 until 2005 by Chevrolet. Mechanics is the physics area concerned with the motions of macroscopic objects. The mean is the number average. To calculate we add up all the numbers then divide by how many numbers there are. In other words it is the sum divided by the count.
[tex]\mu = 8.4 hours[/tex]
[tex]\sigma = 1.8 hours[/tex]
[tex]n=40[/tex]
[tex]z = \frac{Xbar -\mu}{\frac{\sigma}{\sqrt{r} } } = \frac{7.6-8.4}{\frac{1.8}{\sqrt{40} } } = -2.81[/tex]
Therefore the value of Xbar < 7.6 hours. from the standard normal table is 0.0026
Hence, the probability that their mean rebuild time is less than 7.6 hours is 0.0026 = 0.26%.
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