According to a sports & wellness professional, the weight of male individuals aged 30-40 is normally distributed with a mean of 69 kg and a standard deviation of 12 kg.

Based on your case assigned above, solve the following problems using continuous probability distribution techniques.

  • State the variance and how the normal curve will change when the mean increases and the standard deviation decreases.
  • Determine with appropriate calculations if you agree or disagree with the statement that “Less than 5% of the population items lies beyond 2 standard deviations from the population mean.”
  • Calculate the amount for the top and bottom kth percentage of the population, where k is your registration number in your class register. Show all the steps required.
  • Calculate the probability that an individual in the population is more than 5 standard deviations bigger than the population means. Explain if it is possible to find such an individual in the population with reference to your case scenario.