A specific instance of the normal distribution is the standard normal distribution. It is the distribution that develops when the mean and variance of a normal random variable are both equal to one. Standardizing is the process of changing a normal distribution into a standard normal distribution. The following equation can be used to get Z's value:
Z=x-mu/sigma
X ∼ N (50,12²)
Below is a list of how many miles at least 80% of the trucks have driven:
P(X≥x)=P(Z≥x−50/12)
1−P(Z<x−50/12)=0.80
P(Z<x−50/12)=0.20 .
The standard normal distribution table can be used to determine Z's value.
x−50/12=−0.84612
X=−0.84612×12+50
=39.9006
Therefore, at least 80% of the trucks will log 39.9006 thousand miles.
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