1. George throws a ball at a target 25 times. Each time George throws the ball,...

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1. George throws a ball at a target 25 times. Each time George throws the ball, the probability of the ball hitting the target is 0.52 The random variable X represents the number of times George hits the target in 25 throws. (a) Find (i) P (X=12) (ii) P (X 7) George now throws the ball at the target 350 times. (b) Use a normal approximation to calculate the probability that he will hit the target more than 210 times. 2. A manufacturer uses a machine to make metal rods. The length of a metal rod, L cm, is normally distributed with a mean of 9 cm a standard deviation of x cm Given that the proportion of metal rods less than 8.877 cm in length is 5% (a) show that x = 0.075 to 3 decimal places. (b) Calculate the proportion of metal rods that are between 8.92 cm and 9.07 cm in length. The cost of producing a single metal rod is 30p A metal rod where L <8.92 is sold for scrap for 6p where 8.92 L 9.07 is sold for 60p where L > 9.07 is shortened for an extra cost of 12p and then sold for 60p (c) Calculate the expected profit per 600 of the metal rods. Give your answer to the nearest pound. The same manufacturer makes metal hinges in large batches. The hinges each have a probability of 0.02 of having a fault. A random sample of 150 hinges is taken from each batch and the batch is accepted if fewer than 6 hinges are faulty. The manufacturer's aim is for 99% of batches to be accepted. (d) Explain whether the manufacturer is likely to achieve its aim. 1. George throws a ball at a target 25 times. Each time George throws the ball, the probability of the ball hitting the target is 0.52 The random variable X represents the number of times George hits the target in 25 throws. (a) Find (i) P (X=12) (ii) P (X 7) George now throws the ball at the target 350 times. (b) Use a normal approximation to calculate the probability that he will hit the target more than 210 times. 2. A manufacturer uses a machine to make metal rods. The length of a metal rod, L cm, is normally distributed with a mean of 9 cm a standard deviation of x cm Given that the proportion of metal rods less than 8.877 cm in length is 5% (a) show that x = 0.075 to 3 decimal places. (b) Calculate the proportion of metal rods that are between 8.92 cm and 9.07 cm in length. The cost of producing a single metal rod is 30p A metal rod where L <8.92 is sold for scrap for 6p where 8.92 L 9.07 is sold for 60p where L > 9.07 is shortened for an extra cost of 12p and then sold for 60p (c) Calculate the expected profit per 600 of the metal rods. Give your answer to the nearest pound. The same manufacturer makes metal hinges in large batches. The hinges each have a probability of 0.02 of having a fault. A random sample of 150 hinges is taken from each batch and the batch is accepted if fewer than 6 hinges are faulty. The manufacturer's aim is for 99% of batches to be accepted. (d) Explain whether the manufacturer is likely to achieve its aim.