Question

mrs. starnes enjoys doing sudoku puzzles. the time she takes to complete an easy puzzle can be modeled by a normal distribution with mean 5.3 minutes and standard deviation 0.9 minutes. find the 20th percentile of mrs. starness sudoku times for easy puzzles. 5.48 minutes 6.06 minutes 4.54 minutes 4.78 minutes

Explanation:

Step1: Find the z - score

We want to find the \(z\) - score corresponding to the 20th percentile. Using a standard normal table (or a calculator with a normal - distribution function), the \(z\) - score \(z\) such that \(P(Z\lt z)=0.20\). Looking up in the standard normal table, \(z\approx - 0.84\).

Step2: Use the z - score formula

The \(z\) - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 5.3\) (mean) and \(\sigma=0.9\) (standard deviation). We want to solve for \(x\).
Rearrange the formula: \(x=\mu + z\sigma\)
Substitute \(\mu = 5.3\), \(z=-0.84\), and \(\sigma = 0.9\) into the formula:
\(x=5.3+(-0.84)\times0.9\)
\(x = 5.3-0.756\)
\(x = 4.544\approx4.54\)

Answer:

4.54 minutes