ElAlMSIEIAZlT STATISTICS 2 SEMESTER 2 2021.002}! INDIVIDUAL ASSIGNMENT (10%) GROUP 1: Dr. Hannuun Eadiela binti Yaaeoh GROUP 2: Assoc. Prof. Dr Lao Wee Yeap SUBMISSION DATE: 12 APRIL 2022 {11.59pm} Question 1 Let X be a continuous random variable with the following probability density function ex, l] S x S 2 f(x) = i 0, elsewhere a) Evaluate c b) Find F (x) c] Use F(x) to nd PG 5 X S 2) Question 2 The mean daily milk production of a herd of goats has a normal distribution with mean \"ling and standard deviation 13kg. What is the probability that a) the milk production for a goat chosen at random will be less than 60kg? b) the milk production for a goat chosen at random will be greater than 90kg? e) the milk production for a goat chosen at random will be between 60kg and 90kg? Question 3 An assessment test is used to measure a person's readiness for college. The mathematics scores in the test are scaled to have a normal distribution with mean 500 and standard deviation 100. What proportion of the people taking the test will score below 350? Remedial assistance will be given to students in the bottom 10%. What is the maximum score of this group of students? Question 4 A certain type of thread is manufactured with a mean tensile strength of 78.3kg and standard deviation of 5.61:3. Assuming that the strength of this type of thread is distributed approximately normal, find a) the probability that the mean strength of a random sample of It] such thread falls between Wk; and 5'ng b) the value of x to the right of which 15% of the means computed from random samples of size 10 would fall. Question 5 It is known that a particular machine produces 10% defective electrical components. A box of 100 items of these electrical components will be rejected by a buyer if more than [1% of the items are defective. Buyer A ordered 200 boxes of these electrical components. How many of these boxes will be rejected by buyer A? END OF QUESTIONS