Katey is planning her shopping list for Easter and she volunteered to make pies for dinner. Out of all of her family members, she knows from past experience that each family member eats 2 pieces of pie on average with a standard deviation of 0.4 and that the number of pieces of pie eaten by family members is normally distributed. This year a random sample of 18 family members are coming for Easter. Because of the current state of affairs, the pies will be left on the doorsteps for people to grab a slice or two. Katey is hoping to only have to make 4 pies which will end up yielding 32 pieces of pie. What is the probability Katey will have to make more than a total of 32 pieces of pie? Round to four decimal places.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Katey is planning her shopping list for Easter and she volunteered to make pies for dinner. Out of all of her family members, she knows from past experience that each family member eats 2 pieces of pie on average with a standard deviation of 0.4 and that the number of pieces of pie eaten by family members is normally distributed. This year a random sample of 18 family members are coming for Easter.  Because of the current state of affairs, the pies will be left on the doorsteps for people to grab a slice or two.  

Katey is hoping to only have to make 4 pies which will end up yielding 32 pieces of pie. What is the probability Katey will have to make more than a total of 32 pieces of pie?  Round to four decimal places. 

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