Chapter 4, Problem 4.4P

(a)

Interpretation Introduction

Interpretation:

The mean value of ${}^{\text{69}}{\text{Ga/}}^{\text{71}}\text{Ga}$ has to be calculated.

Concept Introduction:

Mean:

The arithmetic mean (also called average) is the most commonly used measure of central tendency. It is calculated by summing the observed numerical values of a variable in a set of data and then dividing the total by the number of observations involved.

Computation of mean:

If $x_1,{\text{ x}}_{\text{2}}\mathrm{.....}{x}_n$ be n values.

The mean value is calculated as,

  $Mean\text{ = }\frac{{\displaystyle \sum _{i=1}^n{x}_i}}{n}$

Here, n is total number of values and ${\displaystyle \sum _{i=1}^n{x}_i}$ represents sum of all given values.

(b)

Interpretation Introduction

Interpretation:

The standard deviation and the relative standard deviation values has to be calculated.

Concept Introduction:

Standard deviation:

The standard deviation of a random variable X of size n is defined as,

$\text{s = }\sqrt{\frac{{\displaystyle \sum _{\text{i=1}}^{\text{n}}{\left({\text{x}}_{\text{i}}\text{-}\overline{\text{x}}\right)}^{\text{2}}}}{\text{n-1}}}$, where ${\text{x}}_{\text{i}}$ is the i^th observation and $\overline{\text{x}}$ is the sample mean.

The standard deviation measures the absolute variability of a distribution.

$\text{RSD = }\frac{S}{\overline{x}}\times 100$, here RSD is relative standard deviation, S is standard deviation and $\overline{\text{x}}$ is mean.

(c)

Interpretation Introduction

Interpretation:

The $\text{99\%}$ confidence interval for sample $8$ has to be calculated.

Concept Introduction:

The confidence interval is determined as follows,

    $\mu =\overline{x}\underset{\_}{+}\frac{ts}{\sqrt{n}}$

Here, $\overline{\text{x}}$ is mean value, s is standard deviation, n is number of values and t is Students, t for $95\%$ confidence and $n-1$ is degrees of freedom.