91Ó°ÊÓ

Time value,$x=3minutes$

Mean,$\mathrm{μ}=5.3minutes$

Standard deviation,$\mathrm{σ}=0.9minute$

The formula used:$z=\frac{x−\mathrm{μ}}{\mathrm{σ}}$

Calculate the $z−$score,

$z=\frac{x−\mathrm{μ}}{\mathrm{σ}}=\frac{3−5.3}{0.9}≈−2.56$

Use the normal probability table in the appendix to get the corresponding probability.

In the usual normal probability table for $P(z<−2.56)$look at the row that starts with $-2.5$and the column that starts with$.06$

$P(x<3)=P(z<−2.56)=0.0052$

Therefore,

Mrs. Starnes solves a simple Sudoku puzzle in under $3$ minutes, or $0.0052$ of the time.

Calculate the $z−$score,

$z=\frac{x−\mathrm{μ}}{\mathrm{σ}}=\frac{6−5.3}{0.9}≈0.78$

To find the equivalent probability, use the normal probability table in the appendix.

The typical normal probability table for $P(z<0.78)$has a row that starts with $0.7$and a column that starts with$.08$

$$\begin{gathered} P(x>6)=P(z>0.78) \\ =1−P(z<0.78) \\ =1−0.7823 \\ =0.2177 \\ =21.77\% \end{gathered}$$

Therefore,

Mrs. Starnes spends more than $6$ minutes on an easy task around $21.77$ percent of the time.

Calculate the $z−$score,

$z=\frac{x−\mathrm{μ}}{\mathrm{σ}}=\frac{6−5.3}{0.9}≈0.78$

Or

$z=\frac{x−\mathrm{μ}}{\mathrm{σ}}=\frac{8−5.3}{0.9}=3.00$

To find the equivalent probability, use the normal probability table in the appendix.

The usual normal probability table for $P(z<0.78)$has a row that starts with $0.7$and a column that starts with$.08$

Or

In the standard normal probability table for $P(z<3.00)$look for the row that starts with $3.0$and the column that starts with$.00$

$$\begin{gathered} P(6<x<8)=P(0.78<z<3.00) \\ =P(z<3.00)−P(z<0.78) \\ =0.9987−0.7823 \\ =0.2164 \\ =21.64\% \end{gathered}$$

Therefore,

Mrs. Starnes takes between $6$ and $8$ minutes to finish $21.64$ percent of the easy Sudoku puzzles.