DRUGS R US is a large manufacturer of various kinds of liqui

\"DRUGS R US\" is a large manufacturer of various kinds of liquid vitamins. The quality control department has noted that the bottles of vitamins marked a ounces vary in content with a standard deviation of b ounces. Assume the contents of the bottles are normally distributed.

a. What percentage of all bottles produced contains more than c ounces of vitamins?
b. What percentage of all bottles produced contains less than d ounces?
c. What percentage of bottles produced contains between e and f ounces?
d. N percent of the bottles will contain at least how many ounces?
e. What percentage of the bottles contains between g and h ounces?

Solution

a) z score = (x- mean)/standard deviation

    mean= a , standard deviation = b

     when x=c, z₁ = (c-a)/b

     P(x > c) = p(z > z₁ ) = 1 - p(z < z₁)

    % of bottles containing more than c ounces = P (x>c) x 100

b) when x=d, z₂ = (d-a)/b

     P(x < d ) = p(z < z₂ )

    % of bottles containing less than d ounces = P (x < d) x 100

c) when x=e, z₃ = (e-a)/b

    when x=f, z₄ = (f-a)/b

    P(e<x<f) = P (z₃ < z < z₄ ) = P (z < z₄ ) - ( 1 - P(z < z₃ ))

   percentage of bottles produced containing between e and f ounces = P(e<x<f) x 100

e)when x=g, z₅ = (g-a)/b

    when x=h, z₆ = (h-a)/b

    P(g<x<h) = P (z₅ < z < z₆ ) = P (z < z₆ ) - ( 1 - P(z < z₅ ))

   percentage of bottles produced containing between e and f ounces = P(g<x<h) x 100