Probability and Statistics

9. (A) According to a published study, 25% of Ghanaian children are stunted. If we randomly sample 15 children from the population, find the probability that stunted children will be a. exactly five (2 marks) b. at least three (2 marks) c. no more than four (2 marks) d. four or more (2 marks) (B) Find the following: a. Area under the standard normal distribution curve between z = 0.24 and z = -1.12 (2 marks) b. z value to the left of the mean so that 60.64% of the area under the distribution curve lies to the right of it (2 marks) (C) A study conducted in Cape Coast that evaluated the relationship between vitamin D intake and pregnancy outcome compute the mean vitamin D intake during the period of pregnancy to be 71.41 ug/day with standard deviation of 50.74 ug/day. Assume that vitamin D intake in this population is normally distributed. 5 a. What proportion of pregnant women in Cape Coast will have a vitamin D intake of less than 25 ug/day? (3 marks) b. What proportion of pregnant women in Cape Coast will have a vitamin D intake of greater than 100 ug/day? (3 marks) c. What proportion of pregnant women in Cape Coast will have a vitamin D intake between 50 and 75 ug/day? (3 marks) d. To be classified as having adequate vitamin D intake, an individual's intake must rank in the top 25%. Find the lowest possible vitamin D intake (3 marks) e. Indicate the use of the Central Limit Theorem (1 mark)