Standard Deviation and Marks
Assignment 1(STA2204)
1. The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this proportion is within 3 percentage points of the true proportion. How large a sample is necessary? (4 marks)
2. The mean number of cups of coffee sold per minute at Relax cafeteria is 3. Assuming that the number of cups of coffee sold is independent of the day, find the probability that (i) exactly 6 cups of coffee are sold from 8.15 am to 8.20 am. (3 marks)
(ii) the cafeteria will sell exactly 8 cups of coffee from 8.15 am to 8.20 am on Monday and Friday. (3 marks)
3. In order to be accepted into a certain top university, applicants must score within the top 5% on the SAT exam. Given that the exam has a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university? (4 marks)
4. In a game, a fair dice is tossed and a person has to pay RM3 to play. If number 1 appears, the person receives RM12. If an even number appears, the person receives RM5 and if other number appears, he will be fined RM6. Let X denotes the gain of a player. Find the expected value of X if a person plays once. (5 marks)
5. The owner of a coffee shop observed that 48% of his customers ordered coffee while the remaining 52% of the customers ordered tea. In a random sample of 6 customers, find the probability that (i) more than 2 customers would order coffee. (3 marks)
(ii) exactly 3 customers would order tea. (3 marks)
1. The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this proportion is within 3 percentage points of the true proportion. How large a sample is necessary? (4 marks)
2. The mean number of cups of coffee sold per minute at Relax cafeteria is 3. Assuming that the number of cups of coffee sold is independent of the day, find the probability that (i) exactly 6 cups of coffee are sold from 8.15 am to 8.20 am. (3 marks)
(ii) the cafeteria will sell exactly 8 cups of coffee from 8.15 am to 8.20 am on Monday and Friday. (3 marks)
3. In order to be accepted into a certain top university, applicants must score within the top 5% on the SAT exam. Given that the exam has a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university? (4 marks)
4. In a game, a fair dice is tossed and a person has to pay RM3 to play. If number 1 appears, the person receives RM12. If an even number appears, the person receives RM5 and if other number appears, he will be fined RM6. Let X denotes the gain of a player. Find the expected value of X if a person plays once. (5 marks)
5. The owner of a coffee shop observed that 48% of his customers ordered coffee while the remaining 52% of the customers ordered tea. In a random sample of 6 customers, find the probability that (i) more than 2 customers would order coffee. (3 marks)
(ii) exactly 3 customers would order tea. (3 marks)