Question #180495

A study discussed that the percent purity of oxygen from a certain supplier yields a mean of 99.61% and a standard deviation of 0.08%. If the distribution of percent purity is said to be in normal distribution, what purity value exceed exactly 5% of the population?


1
Expert's answer
2021-04-14T07:39:16-0400

We need to calculate the value of yy when the P(Yy)=0.05.P(Y\geq y)=0.05. This is computed as follows


P(Yy)=0.05,1P(Yy)=0.05,P(Yy)=0.95,P(Yμσyμσ)=0.95,P(Zyμσ)=0.95,P(Z1.645)=0.95.P(Y\geq y)=0.05, \\ 1-P(Y\leq y) =0.05,\\ P(Y\leq y)=0.95 ,\\P\left(\frac{Y-\mu}{\sigma}\leq \frac{y-\mu}{\sigma}\right)=0.95, \\ P\left(Z\leq\frac{y-\mu}{\sigma}\right)=0.95,\\P(Z\leq 1.645)=0.95.


From the above we know that


yμσ=1.645\frac{y-\mu}{\sigma}=1.645.


Solving for yy we have


y=(1.645)(σ)+μy=(1.645)(\sigma)+\mu.


Substituting the values of μ\mu and

σ\sigma we have the value of yy to be


y=(1.645)(0.08)+99.61y=99.7416.y=(1.645)(0.08)+99.61 \Longrightarrow y=99.7416.


Thus, the purity value that exceeds exactly 5% of the population is 99.7416%.99.7416\%.


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