STA 212A/T Business Statistics II Assignment One 2024 PDF

SCHOOL OF BUSINESS & ECONOMICS SEPTEMBER TRIMESTER 2024 STA 212A/T: BUSINESS STATISTICS II ASSIGNMENT ONE Answer all the Questions Question One The results of a particular examination are given below in summary form: Passed with distinction...

SCHOOL OF BUSINESS & ECONOMICS SEPTEMBER TRIMESTER 2024 STA 212A/T: BUSINESS STATISTICS II ASSIGNMENT ONE Answer all the Questions Question One The results of a particular examination are given below in summary form: Passed with distinction 19% Passed 61% Failed 20% Its known that a candidate gets grade F (fails) if he/she obtains less than 41% while he/she must obtain at least 91 marks in order to pass with distinction. Determine the mean and standard deviation of the distribution of marks assuming this to be normal. (10 marks) Question Two (a) Weekly demand for eggs stocked by Waumini grocers is normally distributed. The mean is 1500 trays and standard deviation is 150 trays. How many trays should be available for a week if Waumini wants to ensure that the probability of running out of stock does not exceed 2.5%? (5 marks) (b) The marks of the students in a certain examination are normally distributed with mean marks as 60% and standard deviation marks as 20%. On this basis, 64% of the students failed. The result was moderated and 75% of the students passed. Find the pass marks before and after the moderation. (5 marks) Question Three (a) Clearly distinguish between the standard error of the mean and the standard error of the proportion. (2 marks) Page 1 of 2 (b) In human engineering and product design, it is often important to consider the weights of people so that airplanes or elevators aren’t overloaded, chairs don’t break, and other such dangerous or embarrassing mishaps do not occur. Given that the population of men has normally distributed weights, with a mean of 63 kg and a standard deviation of 7 kg, find the probability that: (i) If 1 man is randomly selected, his weight is greater than 61kg. (4 marks) (ii) If 15 different men are randomly selected, their mean weight is less than 65 kg. (4 marks) Question Four When asked if grades are “curved” Professor Makanyanga replies that she uses the normal curve as a guide in assigning letter grades to large classes. She first finds the average numerical grade and the standard deviation of the numerical grades, and then assigns the letter grades as follows: Numerical grades (X) interval Grade X ≥ µ + 1.6 σ A µ + 0.8σ ≤ X < µ + 1.6σ B µ - 0.8σ ≤ X < µ + 0.8σ C µ - 1.6σ ≤ X < µ - 0.8σ D X < µ - 1.6σ F i) In a class of 950, approximately how many students will receive each letter grade? Give your answer to the nearest whole number. (8 marks) ii) The professor finds that the class average is 67 with a standard deviation of 8. What is the highest passing numerical score between 0 and 100 that will receive a C? (2 marks) Question Five Given the population of five numbers 3 9 12 3 18 (i) Compute and tabulate the sampling distribution of the mean for samples of size n=2 and show that µ𝑥̅ = µx (5 marks) (ii) Compute and tabulate the sampling distribution of the proportion for samples of size n = 3 if success is defined as getting an odd number. From the distribution obtained show that µ𝑝̅ = p (5 marks) Page 2 of 2