Question: Task 5: Normal approximation for binomial births (9 marks total) In Chelmsford County, the probability that a randomly chosen birth results in a boy is

Task 5: Normal approximation for binomial births

(9 marks total)

  1. In Chelmsford County, the probability that a randomly chosen birth results in a boy is 45% at the local hospital. Over the course of a month, there are 20 births.
  2. Is a normal approximation to the binomial random distribution appropriate here? Show your calculations and explain your choice.(3 marks)
  3. Use the normal approximation to find the following probability. What is the chance that more than 14 of the births are boys?(3 marks)
  4. Use the binomial probability formula to calculate the probability that more than 14 boys are born in these 20 births.(3 marks)

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