ST130_F: Basic Statistics Semester 2 2016: Assignment Due Date: 30/09/16 Total: 50 marks Instructions: Write your group information: Groups should be...

SSTT113300__FF:: BBaassiicc SSttaattiissttiiccss SSeemm eesstteerr 22 22001166:: Assignment Question 1 [3+4+3=10 marks] The number of items rejected daily by a manufacturer because of defects was recorded for the last 25 days. The results are as follows: 21 8 17 22 19 18 19 14 17 11 6 21 25 19 9 12 16 16 10 29 24 6 21 20 25 (A) Construct a frequency distribution for the data using the class intervals 5-9, 1 0-14, 15-19 , 2 0- 24 and 2 5-29 . (B) Calculate the variance of the frequency distribution. (C) Estimate (i) 80 th percentile and (ii) perc entile rank of 21, using a percentile graph. Question 2 [9+6=15 marks] (A) The events A and B are such that and Compute the following: (i) and (ii) and (iii) and (3+3+3=9 marks ) Due Date : 30/09/16 Total : 50 marks Instructions: 1. Please complete this assignment in your group (the group formed in the tutorials). 2. Write your group information : ID, name, with their signature on the cover page of your assignment. Groups should be more than 3, or less or equal to 6. 3. Plagiarized assignment will be awarded a mark of 0 . ( | ) 0.4,P A B  ( | ) 0.25P B A  ( ) 0.12.P A B  ()PA ( ).PB ( ')P A B  ( ' ) .P A B  ()P A B    ( ) ' . P A B  (B) A small town has one fire engine and one ambulance available for emer gencies. The probability that the fire engine is available when needed is 0.97, and the probability that the ambulance is available when called is 0.93. In an event of emergency, find the probability that (i) Neither the ambulance nor the fire engine is availa ble. (ii) That at least one of them is available. (3+3=6 marks ) Question 3 [9+6=15 marks] (A) Daily sales of petrol from the Nabua service station are normally distributed with mean 6300L and the standard deviation 400L. (i) If a daily sale is selected at random, find the probability that it is less than 6200L. (ii) If petrol sales are sampled for 40 days, and the mean is calculated, find the probability that the sample mean is less than 6200L. (iii) Define the Central limit theorem . (3+4+2= 9 marks) (B) A random sample of 16 mid -sized cars tested for fuel consumption gave a mean of 26.4 kilometers per liter with a standard deviation of 2.3 kilometers per liter . i) Assuming that the kilometers per liter giv en by all mid -sized cars have a normal distribution, find a 99% confidence interval for the population mean μ. ii) Suppose the confidence interval obtained in (b)(i) is too wide. How can the width of this interval be reduced? Describe all possible alternatives . Which alternative is the best and why? (3+3=6 marks ) Question 4 [5+5 =10 marks] (A) An architect estimates that the average height of the buildings of 30 or more stories in Suva is at least 500 feet. A random sample of 12 buildings is sel ected, and the heights in feet are shown. At  = 0.025, is there enough evidence to reject the claim? 634 385 411 741 625 515 345 420 435 535 516 482 (B) A survey by Men’s Health magazine stated that 40% of men said the y used alcohol to reduce stress. At test the claim that a random sample of 100 men was selected and 30 said that they used alcohol to reduce stress. Use the P-value method. THE END 0.10,    