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A normal distribution has a mean of 66.9 and a standard deviation of 4.08.

Find the Z-score corresponding to a value of 62.3.

(Round to the nearest hundredth as needed.)

Answer :

The Z-score corresponding to a value of 62.3 in a normal distribution with a mean of 66.9 and a standard deviation of 4.08 is approximately -0.86. The corresponding data value for this Z-score is approximately 62.47.

In order to find the Z-score, we can use the formula Z = (X - μ) / σ, where X is the data value, μ is the mean, and σ is the standard deviation. Substituting the given values, we have Z = (62.3 - 66.9) / 4.08. Calculating this expression, we get Z ≈ -0.86.

The Z-score measures the number of standard deviations a data value is from the mean. A negative Z-score indicates that the data value is below the mean. To find the corresponding data value for a given Z-score, we can rearrange the formula as X = Z * σ + μ. Substituting the calculated Z-score and the given mean and standard deviation, we have X = -0.86 * 4.08 + 66.9. Evaluating this expression, we find that X ≈ 62.47. Therefore, the data value corresponding to a Z-score of -0.86 is approximately 62.47 when the mean is 66.9 and the standard deviation is 4.08.

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