Chapter 2.1, Problem 16E

(a)

To determine

Interpretation of the z − score.

Explanation of Solution

Given information:

z − score,

  $z=1.89$

The z − score describes the number of standard deviations that a value is from the mean.

Negative z − score indicates that the value is below the mean.

Whereas,

Positive z − score indicates that the value is above the mean.

Thus,

According to the sample, 92 texts sent by Alejandroare 1.89 standard deviations above the mean number texts send by the students.

(b)

To determine

Mean of the distribution using the information along with Alejandro’s z − score.

Answer to Problem 16E

Mean of the distribution,

  $\mu =27.45$

Explanation of Solution

Given information:

Value, $x=92$

Standard deviation, $\sigma =34.15$

z − score, $z=1.89$

Calculations:

Calculate the z − score:

  $z=\frac{x-\mu }{\sigma }$

Substitute values,

  $1.89=\frac{92-\mu }{34.15}$

Multiply both sides by 34.15:

  $64.55=92-\mu$

That becomes

  $\mu =92-64.55=27.45$

Since the units of the mean and the data values are same.

Thus,

The mean is 27.45 text messages.