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21 March, 20:09

A department store, on average, has daily sales of $28,372.72. The standard deviation of sales is $2000. On Tuesday, the store sold $34,885.21 worth of goods. Find Tuesday's zscore and was Tuesday's zscore a significantly high value?

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  1. 21 March, 20:28
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    Z-score = 3.26

    Explanation:

    The Z-score formula to employ is given as follows:

    Z = (X - U) : SD ... (1)

    Where,

    Z = the z-score = ?

    X = Tuesday's sales = $34,885.21

    U = Average or mean of daily sales = $28,372.72

    SD = Standard deviation of sales = $2,000

    Substituting each variable into equation (1), we can calculate the z-score as follows:

    Z = ($34,885.21 - $28,372.72) : $2,000

    = $6,512.49 - $2,000

    = 3.26

    The Z-score of 3.26 implies that the Tuesday's sales is 3.26 standard deviation above the mean. Given the empirical rules of 95%, the Tuesday's sales is not significantly higher than 3 standard deviations above the mean.

    Therefore, the sales on Tuesday were good.
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