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The number of widgets produced by a particular machine in one day is approximately normally distributed with mean 85.46 and standard deviation 12.77. What is the 47* percentile?

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Final answer:

The 47th percentile for the distribution of the number of widgets produced is calculated by converting that percentile to a Z-score and then applying the formula X = μ + Zσ, where μ is the mean (85.46) and σ is the standard deviation (12.77).

Step-by-step explanation:

The question asks what the 47th percentile is for a normally distributed number of widgets produced by a machine with a mean of 85.46 and a standard deviation of 12.77. To find the 47th percentile, we first need to use the standard normal (Z) distribution since the distribution of widgets follows a normal pattern. Percentiles in a normal distribution can be found using a Z-table, statistical software, or a calculator capable of providing normal distribution probabilities. The Z-score corresponding to the 47th percentile can be found, and then we use the formula:

X = μ + Zσ

Where:

  • X is the value that corresponds to the percentile we want to find (47th percentile in this case)
  • μ (mu) is the mean of the distribution
  • Z is the Z-score associated with the 47th percentile from the standard normal distribution
  • σ (sigma) is the standard deviation of the distribution

After obtaining the Z-score for the 47th percentile, you plug in the values into the formula to find the specific number of widgets that represents the 47th percentile.

User Justinl
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