## If you counted eight decay events in 10 seconds, would this be convincing evidence that the product should be returned? Explain

1     . Mom and Grandma are each baking chocolate chip cookies. Each gives you two cookies. One of Mom's cookies has 14 chips in it and the other has 11. Grandma's cookies have 6 and 8 chips.

a.   Estimate the mean number of chips in one of Mom's cookies.

b.   Estimate the mean number of chips in one of Grandma's cookies.

c.    Find the uncertainty in the estimate for Mom's cookies.

d.  Find the uncertainty in the estimate for Grandma's cookies.

e.  Estimate how many more chips there are on the average in one of Mom's cookies than in one of Grandma's. Find the uncertainty in this estimate.

2.   You have received a radioactive mass that is claimed to have a mean decay rate of at least 1 particle per second. If the mean decay rate is less than 1 per second, you may return the product for a refund. Let X be the number of decay events counted in 10 seconds.

a.  If the mean decay rate is exactly 1 per second (so that the claim is true, but just barely), what is P(X ≤ 1)?

b.  Based on the answer to part (a), if the mean decay rate is 1 particle per second, would one event in 10 seconds be an unusually small number?

c.   If you counted one decay event in 10 seconds, would this be convincing evidence that the product should be returned? Explain.

d.   If the mean decay rate is exactly 1 per second, what is P(X ≤ 8)?

e.   Based on the answer to part (d), if the mean decay rate is 1 particle per second, would eight events in 10 seconds be an unusually small number?

f.      If you counted eight decay events in 10 seconds, would this be convincing evidence that the product should be returned? Explain

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