The diagram shows normal curves for the probability distributions of $P$ and $Q,$ that each contain $n$ values. Write down a statement comparing:

the interquartile range for $P$ and the interquartile range for $Q.$

The diagram shows normal curves for the probability distributions of $P$ and $Q,$ that each contain $n$ values. The datasets $P$ and $Q$ are merged to form a new dataset denoted by $W.$

Describe the range of $W.$

The diagram shows normal curves for the probability distributions of $P$ and $Q,$ that each contain $n$ values. The datasets $P$ and $Q$ are merged to form a new dataset denoted by $W.$

Is the probability distribution for $W$ a normal curve? Explain your answer.

The diagram shows normal curves for the probability distributions of $P$ and $Q,$ that each contain $n$ values. The datasets $P$ and $Q$ are merged to form a new dataset denoted by $W.$

Copy the diagram above and sketch onto it a curved graph representing the probability distribution for $W.$ Mark the relative positions of ${\mu }_P, {\mu }_Q$ and ${\mu }_W$ along the horizontal axis.

The distributions of the heights of $1000$ women and of $1000$ men both produce normal curves, as shown. The mean height of the women is $160 \mathrm{cm}$ and the mean height of the men is $180 \mathrm{cm}.$ The heights of these women and men are now combined to form a new set of data. Assuming that the combined heights also produce a normal curve, copy the graph opposite and sketch onto it the curve for the combined heights of the $2000$ women and men.

Probability distributions for the quantity of apple juice in $500$ apple juice tins and for the quantity of peach juice in $500$ peach juice tins are both represented by normal curves.
The mean quantity of apple juice is $340 \mathrm{ml}$ with variance $4 {\mathrm{ml}}^2$ and the mean quantity of peach juice is $340 \mathrm{ml}$ with standard deviation $4 \mathrm{ml}.$

Copy the diagram and sketch onto it the normal curve for the quantity of peach juice in the peach juice tins.

Probability distributions for the quantity of apple juice in $500$ apple juice tins and for the quantity of peach juice in $500$ peach juice tins are both represented by normal curves.
The mean quantity of apple juice is $340 \mathrm{ml}$ with variance $4 {\mathrm{ml}}^2,$ and the mean quantity of peach juice is $340 \mathrm{ml}$ with standard deviation $4 \mathrm{ml}.$

Describe the curves' differences and similarities.