question archive A bottler of drinking water fills plastic bottles with a mean volume of 998 milliliters (mL) and standard deviation  The fill volumes are normally distributed

A bottler of drinking water fills plastic bottles with a mean volume of 998 milliliters (mL) and standard deviation  The fill volumes are normally distributed

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A bottler of drinking water fills plastic bottles with a mean volume of 998 milliliters (mL) and standard deviation  The fill volumes are normally distributed. What proportion of bottles have volumes between  and 

Question 20 options:

A: 0.4549

B: 0.0764

C: 0.0823

D: 0.1587

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Given:

  • μ= 998 mL
  • σ = 7 mL

Now;

  • P(988<x<991) = ?

Suing the z score formula such that P(988<x<991) = P(z1<Z<z2), so;

  • z = (x - μ)/σ
  • z1 = (988 - 998)/7
  • z1 = -1.4286
  • z2 = (991 - 998)/7
  • z2 = -1

So;

  • P(988<x<991) = P(-1.4286 <Z< -1)

Note that P(-1.4286 <Z< -1) = P(z<-1) - P(z<-1.4286), using the p-value calculator;

P(z<-1) = 0.158655

P(z<-1.4286) = 0.07656

Thus;

  • P(988<x<991) = P(z<-1) - P(z<-1.4286)
  • P(988<x<991) = 0.158655 - 0.07656
  • P(988<x<991) ~ 0.0823

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