Solution to 1. A company manufactures soaps. The mean mass of the soaps is 300g with variance … - Sikademy
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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.

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Here's the Solution to this Question

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

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

a)


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

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


b)


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

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

-P(Z\le-2.7735)\approx1-0.002773

\approx0.997227

0.997227(100)=100

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

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