SOLUTION: A large department store has on average 448 shoppers in an hour, with a standard deviation of 21 shoppers. (i) What is the probability that a random sample of 49 different shoppin

Algebra ->  Permutations -> SOLUTION: A large department store has on average 448 shoppers in an hour, with a standard deviation of 21 shoppers. (i) What is the probability that a random sample of 49 different shoppin      Log On


   



Question 1171715: A large department store has on average 448 shoppers in an hour, with a standard deviation of 21 shoppers.
(i) What is the probability that a random sample of 49 different shopping hours has a sample mean between 441 and 446?
(ii) What is the probability that the store is packed with 500 or more shoppers in an hour?

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
the std deviation of the sample mean with 49 in a sample is 21/sqrt(49) or 3
z=(x-mean)/sd
for 441, the z value is -7/3; for 446, the z value is -2/3
the probability (and answer) is 0.2427
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for 500, z is (500-448)/21 or > 52/21. That probability is 0.0066.