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Statistics / Understandable Statistics 9 / Chapter 5.3 / Problem 14

Understandable Statistics | 9th Edition | ISBN: 9780618949922 | Authors: Charles Henry Brase, Corrinne Pellillo Brase

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Quota Problem: Archaeology An archaeological excavation at

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QUESTION:

Quota Problem: Archaeology An archaeological excavation at Burnt Mesa Pueblo showed that about 10% of the flaked stone objects were finished arrow points (Source: Bandelier Archaeological Excavation Project: Summer 1990 Excavations at Burnt Mesa Pueblo, edited by Kohler, Washington State University). How many flaked stone objects need to be found to be 90% sure that at least one is a finished arrow point? (Hint: Use a calculator and note that is equivalent to 1 P(0) 0.90, or P(0) 0.10.)

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QUESTION:

Quota Problem: Archaeology An archaeological excavation at Burnt Mesa Pueblo showed that about 10% of the flaked stone objects were finished arrow points (Source: Bandelier Archaeological Excavation Project: Summer 1990 Excavations at Burnt Mesa Pueblo, edited by Kohler, Washington State University). How many flaked stone objects need to be found to be 90% sure that at least one is a finished arrow point? (Hint: Use a calculator and note that is equivalent to 1 P(0) 0.90, or P(0) 0.10.)

ANSWER:

Problem 14

Quota Problem: Archaeology An archaeological excavation at Burnt Mesa Pueblo showed that about 10% of the flaked stone objects were finished arrow points (Source: Bandelier Archaeological Excavation Project: Summer 1990 Excavations at Burnt Mesa Pueblo, edited by Kohler, Washington State University). How many flaked stone objects need to be found to be 90% sure that at least one is a finished arrow point? (Hint: Use a calculator and note that is equivalent to , or .)

Step by step solution

Step 1 of 2

It’s given that an archaeological excavation at Burnt Mesa Pueblo showed that about 10% of the flaked stone objects were finished arrow points, ie;

We need to determine the minimum sample size needed such that the mean is greater than 1.

……………………..(1)

We know that the mean of a binomial distribution is the product of the number of trials and the probability of success, ie;

number of trials =

probability of success =

we can write (1) as,

(substituting the value of )

(dividing each side by 0.10 ).

So the sample size needs to be at least 10.

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