. \"DRUGS R US\" is a large manufacturer of various kinds of liquid vitamins. Th

Question

. "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 6 ounces vary in content with a standard deviation of 0.3
ounces. Assume the contents of the bottles are normally distributed.


a. What percentage of all bottles produced contains more than 6.51 ounces of vitamins?






b. What percentage of all bottles produced contains less than 5.415 ounces?






c. What percentage of bottles produced contains between 5.46 and 6.495 ounces?






d. Ninety-five percent of the bottles will contain at least how many ounces?




e. What percentage of the bottles contains between 6.3 and 6.6 ounces?

Explanation / Answer

= 6

=0.3

a) P(X>6.51) = P(Z> (6.51-6)/0.3) = P(Z>1.7) = P(Z<-1.7) = 0.0446

b)  P(X<5.415) = P(Z< (5.415-6)/0.3) = P(Z<-1.95) = 0.0256

c)  P(5.46<X<6.495) = P((5.46-6)/0.3<Z< (6.495-6)/0.3) = P(-1.8<Z<1.65) = P(Z<1.65) - P(Z<-1.8) = 0.9505-0.0359= 0.9146

d) P(Z<z) = 0.95 or z = 1.645

so x = 6 + 1.645*0.3 = 6.4935 ounces of vitamins

e) P(6.3<X<6.6) = P((6.3-6)/0.3<Z< (6.6-6)/0.3) = P(1<Z<2) = P(Z<2) - P(Z<1) =0.9772-0.8413 = .1359 = 13.59%  

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