Question

The sales department has determined that the average purchase value for their catalog business is normally distributed with a mean of $30.44 and a standard deviation of $14.99. What is the purchase value at the 20th percentile

Answer 1

The purchase value at the 20th percentile is $17.85 for the distribution with a mean of $30.44 and a standard deviation of $14.99.

How to calculate Z-score to raw score X?

The formula for the X is

X = μ + Z × σ

where,

Z- score, μ is the mean, and σ is the standard deviation

Calculation:

It is given that,

μ = $30.44

σ = $14.99

x% is given as the 20th percentile

So, α = 0.20

then, the Z score from the normal distribution table is -0.84

On substituting,

X = μ + Z × σ

  = 30.44 + (-0.84 × 14.99)

  = 30.44 - 12.59

  = 17.85

Therefore, the purchase value at the 20th  percentile is $17.88.

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