test2 - (i State the distribution of X and give your...

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STA2023 Class Test 2, Tuesday 12 October 1. Suppose that 2% of the population of a rural county in Wyoming believe that OJ Simpson trial resulted in justice being served. Also, suppose I have randomly and independently sampled 200 of these residents. Let X be the number of people in the sample who believe that OJ Simpson trial resulted in justice being served. (i) State the distribution of X and give your reason. (ii) Find the mean value and standard deviation of X. 2. Suppose four balls are randomly selected without replacement from a bag that contains a total of eight balls, five red and three white. Let X be the number of white balls in the four selected balls.
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Unformatted text preview: (i) State the distribution of X and give your reason. (ii) Write down all the possible values of X and the corresponding probabilities. (iii) Find E(X) and Var(X). 3. Suppose X is a normal random variable with mean μ and standard deviation σ . Find the constant δ such that the probability P( μ-δσ < x < μ + δσ29 is equal to (i) 90% (ii) 95% (iii) 99% 4. The diameter of ball bearing produced in a manufacturing process can be assumed to have a uniform distribution over the interval 3.5 to 5.5 millimeters. What is the proportion of ball bearings that have a diameter less than 5 millimeters?...
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