Question
In: Statistics and Probability
The masses of bottles produced by the Guinness factory in Ireland have a mean of 200...
The masses of bottles produced by the Guinness factory in
Ireland have a mean of 200 grams. Suppose the variance of the
bottles is 175 grams. Round all answers to 3 decimals.
a. What is the probability that the mass of a randomly selected
bottle is between 185 and 215 grams? If you can compute the exact
probability, do so. If you cannot, then use an appropriate
approximation.
b. Suppose that we have a sample of 34 bottles. What is the
probability that the sample average mass is between 198.87 and
201.13 grams? If you can compute the exact probability, do so. If
you cannot, then use an appropriate approximation.
Solutions
Expert Solution
Note: P(a<Z<b)=P(Z<b)-P(Z<a)
Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(1.1339, TRUE)" & "=NORM.S.DIST(-1.1339, TRUE)" to find the probability.
Round the value to 3 decimal places.
 |
--------------------------------------------------------------------------------------------------------------------
Note: P(a<Z<b)=P(Z<b)-P(Z<a)
Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(0.4832, TRUE)" & "=NORM.S.DIST(-0.4832, TRUE)" to find the probability.
 |
orchestra answered 1 year agoRelated Solutions
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