Dean Chalmers and Julian Gilbey Solutions for Chapter: The Normal Distribution, Exercise 4: EXERCISE 8A

The probability distributions for $A$ and $B$ are represented in the diagram. Indicate whether each of the following statements is true or false.

${\mu }_A>{\mu }_B$

The probability distributions for $A$ and $B$ are represented in the diagram. Indicate whether each of the following statements is true or false.

${\sigma }_A<{\sigma }_B$

The probability distributions for $A$ and $B$ are represented in the diagram. Indicate whether each of the following statements is true or false.

$A$ and $B$ have the same range of values.

The probability distributions for $A$ and $B$ are represented in the diagram. Indicate whether each of the following statements is true or false.

${\sigma }_A^2={\sigma }_B^2$

The probability distributions for $A$ and $B$ are represented in the diagram. Indicate whether each of the following statements is true or false.

At least half of the values in $B$ are greater than ${\mu }_A.$

The probability distributions for $A$ and $B$ are represented in the diagram. Indicate whether each of the following statements is true or false.

The values in two datasets, whose probability distributions are both normal curves, are summarised by the following totals:
$\Sigma x^2=35000, \Sigma x=12000$ and $n=5000.$
$\Sigma y^2=72000, \Sigma y=26000$ and $n=10000.$

Show that the centre of the curve for $y$ is located to the right of the centre of the curve for $x.$

The values in two datasets, whose probability distributions are both normal curves, are summarised by the following totals:
$\Sigma x^2=35000, \Sigma x=12000$ and $n=5000.$
$\Sigma y^2=72000, \Sigma y=26000$ and $n=10000.$

On the same diagram, sketch a normal curve for each dataset.