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Answer :
To find the value of X above which there is a 40% chance, we need to use the Z-score formula. The Z-score formula is Z = (X - μ) / σ, where Z is the standard score, X is the raw score, μ is the mean, and σ is the standard deviation.
First, we convert the 40% probability to a Z-score using a Z-table or calculator. Since we want to find the value above which there is a 40% chance, we need to find the Z-score that corresponds to a cumulative probability of 1 - 0.40 = 0.60.
Next, we solve the equation for X using the formula X = Z * σ + μ. We substitute the Z-score we found in the previous step, the given standard deviation σ = 8, and the mean μ = 50 into the equation to find the value of X.
Therefore, the value of X above which there is a 40% chance is X = (Z * σ) + μ.
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