The highest common factor of 98 and 42
2 answers:
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Answer:
85.31% probability that their mean rebuild time exceeds 8.1 hours.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
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.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.1 hours.
This is 1 subtracted by the pvalue of Z when X = 8.1. So
By the Central Limit Theorem
has a pvalue of 0.1469
1 - 0.1469 = 0.8531
85.31% probability that their mean rebuild time exceeds 8.1 hours.
Remember
(√a)(√b)=√(ab)
and
so
![( \sqrt[5]{x^4})( \sqrt[5]{x^4} )](https://tex.z-dn.net/?f=%28%20%5Csqrt%5B5%5D%7Bx%5E4%7D%29%28%20%5Csqrt%5B5%5D%7Bx%5E4%7D%20%20%29)
=
![\sqrt[5]{(x^4)(x^4)}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B%28x%5E4%29%28x%5E4%29%7D)
4+4=8
![\sqrt[5]{x^8}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7Bx%5E8%7D)
=
![( \sqrt[5]{x^5})( \sqrt[5]{x^3} )](https://tex.z-dn.net/?f=%28%20%5Csqrt%5B5%5D%7Bx%5E5%7D%29%28%20%5Csqrt%5B5%5D%7Bx%5E3%7D%20%20%29)
=
![x\sqrt[5]{x^3}](https://tex.z-dn.net/?f=x%5Csqrt%5B5%5D%7Bx%5E3%7D%20)
(√a)(√b)=√(ab)
and
so
4+4=8