AAMS2613: In a recent study, a group of 50 patients with knee problems, 11 of them reported symptomatic relief with a specific medication: Probability and Statistics Assignment, TARUC, Singapore

QUESTION 1

• In a recent study, a group of 50 patients with knee problems, 11 of them reported symptomatic relief with a specific medication. If the medication is given to 10 new patients with knee problems, find the probability that it is effective in
  (i) exactly 5 patients,
  (ii) at most 2 patients. 
• The number of ambulance vehicles arriving at a private hospital in a day has a Poisson distribution with an average of 5.4. Determine the probability that the number of ambulance vehicles arriving at the emergency room of a private hospital will be
  (i) exactly three in a day,
  (ii) at most three in two days,
  (iii) at least two in half a day.
• Barbnabbie dolls sold in a month from a large toy shop is normally distributed with a mean of 236 units and a standard deviation of 43 units.
  (i) If the dolls are selected randomly, what is the probability that the Barbnabbie dolls sold is less than 220 units? (3 marks)
  (ii) If 4% of the production is discarded due to defective parts, determine the number of units sold if it falls below the minimum acceptable number.

QUESTION 2

• In a sample of 400 insurance applicants, 3% are known to have hypertension and are taking medication. What is the probability that more than 5% are with hypertension and are taking medication?
• A researcher wishes to study the mean monthly expenses of the adults in Kota Kinabalu. A random sample of 85 adults is selected and they spend an average of RM1533 per month with a standard deviation of RM68. Find a 98% confidence interval for the mean monthly expenses of all adults in Kota Kinabalu.
• A survey was conducted to determine the proportion of dessert shops that sold fresh fruits. From a random sample of 255 dessert shops across Malaysia, 153 sold fresh fruits as part of their menu. Obtain a 94% confidence interval for the population proportion.