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Answer:
4.46% probability that the pressure will exceed this value.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be 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.
Gaussian distribution with a mean value of 69 psi and a standard deviation of 10 psi.
Gaussian distribution = normal.
This means that
If it is important that the pressure stays below 86 psi, what is the probability (in percent) that the pressure will exceed this value?
As a proportion, this probability is 1 subtracted by the pvalue of Z when X = 86. So
has a pvalue of 0.9554
1 - 0.9554 = 0.0446
0.0446*100 = 4.46%
4.46% probability that the pressure will exceed this value.