The Sadaf Company of Los Angeles, California uses an automated filling machine t
ID: 3272303 • Letter: T
Question
The Sadaf Company of Los Angeles, California uses an automated filling machine to fill jars with its Russian-style zucchini spread known as ikra. The filling process is normally distributed with a mean of 19.4 ounces and a standard deviation of 0.15 ounces. (The fill level listed on jars is 19 ounces.)
(a) What is the probability that the fill level of a jar is greater than 19.8 ounces?
(b) If all jars that contain less than 19 ounces or more than 19.9 ounces are rejected for sale, what proportion of jars will be rejected?
(c) What is the probability that for a sample of ten jars, the sample mean will be between 19 ounces and 19.9 ounces?
Explanation / Answer
a) P(X>19.8)
= P(z>(19.8-19.4)/0.15)
= 0.00383
b) P(X<19)+P(X>19.9)
= P(Z<(19-19.4)/0.15)+P(Z>(19.9-19.4)/0.15)
= 0.004259
c) P(19<X<19.9
= P((19-19.4)/0.15)*Sqrt(10)<Z<(19.9-19.4)/0.15)*Sqrt(10)
= 1
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