3. Answer the following questions about normal distributions. Note:Question 3a) and 3b) are different questions which are not related/linked to one another (8 marks grand total):

a)A team of biomedical researchers collected data on the ages of individuals hospitalized due to a respiratory condition over a one-year period. The age distribution followed a normal distribution, with a mean age of =65 and a standard deviation of =5. Please answer the following two questions using the unit normal table (to be eligible for full marks, please show all of your work): (4 marks total)

(i) What percentage of hospitalized individuals were between the ages of 61 and 71? (2 marks)

(ii) What percentage of hospitalized individuals were older than 71? (2 marks)

b) A sample of n = 16 scores is selected from a normally distributed population with a mean of =50 and a standard deviation of =12. Please answer the following two questions using the unit normal table (to be eligible for full marks, please show all of your work): (4 marks total)

(i)What is the probability that the sample mean will be greater than 53?(2 marks) (ii) What is the probability that the sample mean will be less than 44?(2 marks)