If f(x) = 3x + 10x and g(x) = 2x - 4, find (f+ g)(x).
1 answer:
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Answer:
0.0026 = 0.26% probability that the manufacturing line will be shut down unnecessarily
Step-by-step explanation:
We need to understand the normal probability distribution and the central limit theorem to solve this question.
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 normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
What is the probability that the manufacturing line will be shut down unnecessarily?
Less than 0.73 or more than 0.77.
Less than 0.73
pvalue of Z when X = 0.73
By the Central Limit Theorem
has a pvalue of 0.0013
More than 0.77
has a pvalue of 0.9987
1 - 0.9987 = 0.0013
2*0.0013 = 0.0026
0.0026 = 0.26% probability that the manufacturing line will be shut down unnecessarily
To solve this you can multiply the white paint by 
to find the amount of red paint to add which is 32/7 oz or roughly 4.5 oz