Question

In one region of the country, the household credit card debts are approximately normally distributed with a mean of $16,125 and a standard deviation of $7,875. Find the amount of debt corresponding to 32nd percentile of size-81 means of household credit card debts.

Answer 1

$12424

Explanation:

Given that:

Mean (μ) = $16,125, Standard deviation (σ) = $7,875.

The z score corresponding to the 32nd percentile from the normal distribution table is -0.47. That means that the z score of -0.47 = 0.32 = 32nd percentile.

The z score is given by the equation:

`z=(x-\mu)/(\sigma)`, where x is the raw score

Substituting the values and calculating for x:

`z=(x-\mu)/(\sigma) \\-0.47=(x-16125)/(7875)\\ x-16125=-3701.25\\x=-3701.25+16125=12423.75\\`

x ≈ 12424

The debt corresponding to the 32nd percentile is $12424