Answer to Question #304118 in Statistics and Probability for Eddie

Question #304118

1.     A company manufactures soaps. The mean mass of the soaps is 300g with variance 52g. A sample of 100soaps was selected.

a)     Find the probability of selecting soaps more than masses 320g.

b)     How many soaps will have masses between 280g and 500g.

 


1
Expert's answer
2022-03-01T15:47:18-0500

Let X=X= mass of the soap: XN(μ,σ2).X\sim N(\mu, \sigma^2).

Given μ=300 g,σ=52 g.\mu=300\ g, \sigma=\sqrt{52}\ g.

a)


P(X>320)=1P(Z32030052)P(X>320)=1-P(Z\le\dfrac{320-300}{\sqrt{52}})

1P(Z2.7735)0.002773\approx1-P(Z\le2.7735)\approx0.002773


b)


P(280<X<500)=P(Z<50030052)P(280<X<500)=P(Z<\dfrac{500-300}{\sqrt{52}})

P(Z28030052)P(Z27.7350)-P(Z\le\dfrac{280-300}{\sqrt{52}})\approx P(Z\le27.7350)

P(Z2.7735)10.002773-P(Z\le-2.7735)\approx1-0.002773

0.997227\approx0.997227

0.997227(100)=1000.997227(100)=100

100 soaps will have masses between 280g and 500g.



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