91Ó°ÊÓ

Value,$x=22$

Standard deviation, $\mathrm{σ}=9.42$

$z−$ score,$z=1.10$

The formula used:$z=\frac{(value-mean)}{(s\tan darddeviation)}$

The amount of standard deviations a value deviates from the mean is described by the $z-$score.

A value below the mean is indicated by a negative $z-$score.

Whereas,

The value above the mean is indicated by a positive $z-$score.

Thus,

Jackson owns $22$ pairs of shoes, which is $1.10$standard deviations more than the mean number of pairs owned by the other students, according to the sample.

Calculate the z − score:

$z=\frac{x−\mathrm{μ}}{\mathrm{σ}}$

Substitute values,

$1.10=\frac{22−\mathrm{μ}}{9.42}$

Multiply both sides by 9.42:

$10.362=22−\mathrm{μ}$

That becomes

$\mathrm{μ}=22−10.362=11.638$

Because the data values and the mean units are the same.

Thus,

The mean is $11.638$ pairs of shoes.