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Cereal Box Weights: Z-Scores, Probabilities & Truth Behind Claims
Chapter 7, Problem 56(choose chapter or problem)
A company’s cereal boxes advertise 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean \(\mu=9.70\) ounces and standard deviation \(\sigma=0.03\) ounces.
(a) What is the probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal? Show your work.
(b) Now take an SRS of 5 boxes. What is the probability that the mean amount of cereal \(\bar{x}\) in these boxes is 9.65 ounces or less? Show your work.
Questions & Answers
QUESTION:
A company’s cereal boxes advertise 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean \(\mu=9.70\) ounces and standard deviation \(\sigma=0.03\) ounces.
(a) What is the probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal? Show your work.
(b) Now take an SRS of 5 boxes. What is the probability that the mean amount of cereal \(\bar{x}\) in these boxes is 9.65 ounces or less? Show your work.
ANSWER:Step 1 of 8
(a)
Given:
\(\begin{array}{l} \mu=\text { Mean }=9.70 \\ \sigma=\text { Standard deviation }=0.03 \\ x=9.65 \end{array}\)
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Cereal Box Weights: Z-Scores, Probabilities & Truth Behind Claims
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Explore the intricacies of evaluating cereal box weights using Z-scores and normal distribution. By examining both individual boxes and a sample mean, understand the probabilities of achieving certain weight values. Gain insights into how statistical tools help interpret real-world product claims.