A delivery service claims that orders arrive before noon 90% of the time. If Amy uses the delivery service 20 times, how many times can she predict the deliveries will arrive before noon? Is the claim accurate if her packages arrive after noon 4 times?

Question

Mathematics

Azkaban

26 February, 21:47

A delivery service claims that orders arrive before noon 90% of the time. If Amy uses the delivery service 20 times, how many times can she predict the deliveries will arrive before noon? Is the claim accurate if her packages arrive after noon 4 times?

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Kadyn Lin · Answer 1

They claim that 90% of the times, the orders arrive in time.

Then, out of N orders, (90%/100%) * N of them will arrive in time.

Here we have that N = 20

then the number that arrives in time is:

(90%/100%) * 20 = 18

Now, experimetally we see that 4 times her packages arrived after noon (so 16 times the packages arrived in time), so we can calculate the experimental percentage as:

(X/100%) * 20 = 16

X = (16/20) * 100% = 80%

so the percentages doesn't match, so it the claim is not really accurate, but this is a small sample, so if the number of times that she uses the delivery increases, we may see that the experimental percentage gets closer to the claimed percentage.