1 Chocolate chip cookies have a distribution that is approximately normal with a
ID: 3135011 • Letter: 1
Question
1 Chocolate chip cookies have a distribution that is approximately normal with a mean of 23.7 chocolate chips per cookie and a standard deviation of 2.8 chocolate chips per cookie. For quality control purposes, a manufacturer wants to make sure that the number of chocolate chips stays within reasonable limits. Production has been set to keep the number of chips at or below the 90th percentile. Therefore, any cookie with a chip count in the top ten percentile will be set aside for evaluation. What is the maximum number of chips that a cookie should have to meet the requirements of quality control?
2 SAT scores are normally distributed with a mean score of 1497 and a standard deviation of 322. Ohio State has an average score of 1864. If 40 student applicants are randomly selected, what is the probability that their average SAT score is greater than 1864?
3 Assume that the Richter scale magnitudes of earthquakes are normally distributed with a mean of 1.182 and a standard deviation of 0.579. Earthquakes with a magnitude above 4.0 will cause indoor items to shake. What percentage of earthquakes fall into this category?
Explanation / Answer
1.
First, we get the z score from the given left tailed area. As
Left tailed area = 0.9
Then, using table or technology,
z = 1.281551566
As x = u + z * s,
where
u = mean = 23.7
z = the critical z score = 1.281551566
s = standard deviation = 2.8
Then
x = critical value = 27.28834438 [ANSWER]
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