Weight of bananas follow Normal distribution with mean 121 gram and standard deviation of 17 grams .
Thus X~ N ( =121 , =17 )
The store receives weekly shipment of 6 bananas . Thus n = 6
The store owner reject the shipment if the average weight is below 117.53 g
Thus Probability of Rejecting shipment is given by P ( < 117.53 )
Now we need to find the Probability that the next shipment of bananas is accepted .
So required probability is given by
Pr( shipment of bananas is accepted ) = 1 - Pr ( shipment of bananas is Rejected )
= 1 - P ( < 117.53 )
= 1 - P ( < )
= 1 - P ( Z < )
Pr( shipment of bananas is accepted ) = 1 - P ( Z < -0.4999841 )
where Z ~ N(0,1)
Now P ( Z < -0.4999841 ) can be obtained from standard normal probability table or more accuratly from any software like R/Excel
From R
>
pnorm(Z)
# P ( Z < -0.4999841 )
[1] 0.3085431
Hence P ( Z < -0.4999841 ) = 0.3085431
Pr( shipment of bananas is accepted ) = 1 - P ( Z < -0.4999841 )
= 1 - 0.3085431 = 0.6914569
Pr( shipment of bananas is accepted ) = 0.6914569 0.6915
So correct option is
Option e) 0.6915
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