The weights of packets of cheese are normally distributed with mean 200 grams and standard deviation 5 grams.Thirty (30) % of packets have a weight greater than Y.Find Y, correct to the nearest gram.
Question
The weights of packets of cheese are normally distributed with mean 200 grams and standard deviation 5 grams.Thirty (30) % of packets have a weight greater than Y.Find Y, correct to the nearest gram.
Solution
To find the value of Y such that 30% of the packets have a weight greater than Y, we need to determine the corresponding z-score for the 70th percentile (since 100% - 30% = 70%).
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Identify the mean (μ) and standard deviation (σ):
- Mean (μ) = 200 grams
- Standard deviation (σ) = 5 grams
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Find the z-score for the 70th percentile:
- Using a standard normal distribution table or a calculator, the z-score corresponding to the 70th percentile is approximately 0.524.
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Use the z-score formula to find Y:
- The z-score formula is:
- Rearrange the formula to solve for Y:
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Substitute the values into the formula:
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Round Y to the nearest gram:
- grams
Therefore, the value of Y, correct to the nearest gram, is 203 grams.
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