Solution:
We are given
µ = 284, σ = 22, n = 14
We have to find the value of ‘a’ such that P(Xbar>a) = 2% = 0.02
P(Xbar>a) = 0.02
P(Xbar<a) = 1 – P(Xbar>a) = 1 – 0.02 = 0.98
P(Xbar<a) = 0.98
Critical value Z for probability 0.98 is given as Z = 2.053749 (by using z-table or excel).
We have
a = µ + Z*[σ/sqrt(n)]
a = 284 + 2.053749*(22/sqrt(14))
a = 284 + 2.053749*5.879747
a = 284 + 12.07552
a = 296.0755
Required Answer: 296 gram
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