The weights of kiwifruit picked from a Te Puke orchard are approximately normally distributed with mean 65 g and standard deviation 8 g.
Figure 1 sketches this model, with the weights 50 g, 55 g and 75 g marked on the axis.
Sketch of a normal curve with mean 65 g and standard deviation 8 g; the weights 50, 55 and 75 g are marked on the horizontal axis and the region between 55 g and 75 g is shaded.Facts you may need
(a)
Find the proportion of kiwifruit that weigh between 55 g and 75 g.
(b)
Find the weight that is exceeded by 25% of the kiwifruit.
(c)
Kiwifruit under 50 g are rejected at the packhouse. Out of 10 000 kiwifruit from this orchard, how many are expected to be rejected? Comment on how reliable the model is likely to be for this calculation.
