Chapter 3.2, Problem 3.26E

(a)

To determine

To calculate the percent of values that falls less than 2.1 pounds.

Answer to Problem 3.26E

84% of the values

Explanation of Solution

Given:

Mean = 2 pounds

Standard deviation = 0.1 pound

Concept used:

As per empirical rule

1. 68% of the data falls within one standard deviation from the mean.
2. 95% of the data falls within two standard deviations from the mean.
3. 99.7% of the data falls within three standard deviations from the mean.

Calculation:

  $\begin{array}{c}z=\frac{2.1-2}{0.1}\\ =\frac{0.1}{0.1}\\ =1\end{array}$

The proportion of values that fall less than one standard deviation above from the mean. $50\%+34\%=84\%$. The 84% of the values falls less than one standard deviation above from the mean.

(b)

To determine

To calculate the percent of values that falls less than 1.8 pounds.

Answer to Problem 3.26E

2.5% of the values

Explanation of Solution

Calculation:

  $\begin{array}{c}z=\frac{1.8-2}{0.1}\\ =\frac{-0.2}{0.1}\\ =-2\end{array}$

The proportion of values that fall less than two standard deviationsbelow from the mean $2.35\%+0.15\%=2.5\%$.The 2.5% of the values falls less than two standard deviationsbelow from the mean.

(c)

To determine

To calculate the percent of values that falls more than 1.9 pounds.

Answer to Problem 3.26E

84% of the values

Explanation of Solution

Calculation:

  $\begin{array}{c}z=\frac{1.9-2}{0.1}\\ =\frac{-0.1}{0.1}\\ =-1\end{array}$

The proportion of values that fall more than one standard deviation above from the mean $34\%+50\%=84\%$.The 84% of the values more than one standard deviation above from the mean.