Paul the "Psychic" Octopus rose to fame in 2010 after his feeding behaviour correctly predicted the winner of many soccer matches in the World Cup. Paul's cousin, Henry is a less successful "psychic" octopus, predicting the winner of soccer matches with only 65% accuracy. If Henry is to choose winners for the next 9 soccer matches,

33. What is the probability that Henry will correctly predict the winner of all 9 matches?

a) 0.0101 b) 0.0001 c) 0.0424 d) 0.0207

34. What is the probability that Henry will correctly predict the winner of at least 7 matches?

a) 0.4628 b) 0.3373 c) 0.2162 d) 0.0112

35. What is the probability that Henry will correctly predict the winner of no more than 3 soccer matches?

a) 0.0536 b) 0.0535 c) 0.6089 d) 0.5882

36. What is the expected number of correct predictions and standard deviation of correct predictions?

= 1.0665= 2.0475= 1.4309

1. a)E(x) = 2.41,
2. b)E(x) = 6.50,
3. c)E(x) = 5.85,
4. d)E(x) = 5.85,

= 2.0475

37. In its standardised form, the normal distribution:

a) has a mean of 0 and a standard deviation of 1.

b) hasameanof1andavarianceof0.

c) has an area equal to 0.5.

d) cannot be used to approximate discrete probability distributions.