Question: Collette is self-employed, selling cosmetics at home parties. She wants to estimate if the average amount a client spends at each party is enough to be profitable. She assumes that she cannot make ends meet if it is less than $32. If a random sample of 25 receipts has been measured, what is the probability that the average amount a client spent x̄ is less than $32? Assume that the distribution of the amount spent per client is normal, the population mean is μ = $34.70, and the standard deviation is σ = $4.85.

Transform x̄ into its respective Z-score. Show your calculations.

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