A student is investigating the numbers of cherries in a Rays fruit cake. A random sample of Rays fruit cakes is taken and the results are shown in the table below.
Number of cherries
0
1
2
3
4
5
\(\geqslant 6\)
Frequency
24
37
21
12
4
2
0
Calculate the mean and the variance of these data.
Explain why the results in part (a) suggest that a Poisson distribution may be a suitable model for the number of cherries in a Rays fruit cake.
The number of cherries in a Rays fruit cake follows a Poisson distribution with mean 1.5 A Rays fruit cake is to be selected at random.
Find the probability that it contains
exactly 2 cherries,
at least 1 cherry.
Rays fruit cakes are sold in packets of 5
Show that the probability that there are more than 10 cherries, in total, in a randomly selected packet of Rays fruit cakes, is 0.1378 correct to 4 decimal places.
Twelve packets of Rays fruit cakes are selected at random.
Find the probability that exactly 3 packets contain more than 10 cherries.
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