Answer :
The standard deviation is $42.96.
The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard deviation. There are three ways to find the z-score that corresponds to a given area under a normal distribution curve 1. Use the z-table. 2. Use the Percentile to Z-Score Calculator.
Given : 75% of all families spend more than $75 weekly for food,
Mean = μ = $104
We have to find standard deviation σ.
75% of all families spend more than $75 weekly for food
For 100 - 75 = 25%, z = -0.675
Now, z = (x - μ) / σ
∴ σ = (x - μ) / z
σ = (75 - 104)/-0.675
= -29/-0.675
= 42.96
Thus, the standard deviation is $42.96.
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