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In a normal distribution,%31 of the items are under45 and%8 are over64 . Find the mean and standard deviation of thedistribution. (Given that,19.0)5.0( f42.0)4.1( f

Question

In a normal distribution,%31 of the items are under45 and%8 are over64 . Find the mean and standard deviation of thedistribution. (Given that,19.0)5.0( f42.0)4.1( f

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Solution

The problem you've presented is a statistics problem involving a normal distribution. However, the problem seems to be incomplete or incorrectly formatted, as the given information "(Given that,19.0)5.0( f42.0)4.1( f" is unclear.

In a normal distribution, the mean (μ) is the center of the distribution and the standard deviation (σ) measures the spread of the distribution.

Given that 31% of the items are under 45 and 8% are over 64, we can use the Z-score formula to find the mean and standard deviation. The Z-score is a measure of how many standard deviations an element is from the mean.

The Z-score formula is Z = (X - μ) / σ, where X is the element, μ is the mean, and σ is the standard deviation.

However, to use this formula, we need the Z-scores for the given percentages, which are typically found in a Z-table or can be calculated using statistical software.

Once we have the Z-scores, we can set up two equations based on the Z-score formula (one for the 31% under 45 and one for the 8% over 64) and solve for the mean and standard deviation.

Unfortunately, without the Z-scores or additional information, we cannot solve this problem. Please provide the complete information.

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