Write down the median weight of the rats.

Find the percentage of rats that weigh 70 grams or less.

The same data is presented in the following table.

Write down the value of $p$.

The same data is presented in the following table.

Find the value of $q$.

The same data is presented in the following table.

Use the values from the table to estimate the mean and standard deviation of the weights.

Assume that the weights of these rats are normally distributed with the mean and standard deviation estimated in part (c).

Find the percentage of rats that weigh 70 grams or less.

Assume that the weights of these rats are normally distributed with the mean and standard deviation estimated in part (c).

A sample of five rats is chosen at random. Find the probability that at most three rats weigh 70 grams or less.

50 (g)     A1     N1

[2 marks]

65 rats weigh less than 70 grams     (A1)

attempt to find a percentage     (M1)

eg     $\frac{{65}}{{80}},{\text{ }}\frac{{65}}{{80}} \times 100$

81.25 (%) (exact), 81.3     A1     N3

[2 marks]

$p = 10$     A2     N2

[2 marks]

subtracting to find $q$     (M1)

eg     $75 - 45 - 10$

$q = 20$     A1     N2

[2 marks]

evidence of mid-interval values     (M1)

eg     $15, 45, 75, 105$

$\overline x  = 52.5$   (exact), $\sigma  = 22.5$   (exact)     A1A1     N3

[3 marks]

0.781650

78.2   (%)     A2     N2

[2 marks]

recognize binomial probability     (M1)

eg     $X \sim {\text{B}}(n,{\text{ }}p)$, $\left( \begin{array}{c}5\\r\end{array} \right)$ $\times {0.782^r} \times {0.218^{5 - r}}$

valid approach     (M1)

eg     ${\text{P}}(X \leqslant 3)$

$0.30067$

$0.301$     A1     N2

[3 marks]