Suppose that the actual amount of instant coffee that a filling machine puts into “6-ounce” jars is a random variable having a normal distribution with σ = 0.05 ounce. If only 3 percent of the jars are to contain less than 6 ounces of coffee, what must be the mean fill of these jars?
Answer to relevant QuestionsCheck in each case whether the normal approximation to the binomial distribution may be used according to the rule of thumb on page 192. (a) n = 16 and . = 0.20; (b) n = 65 and . = 0.10; (c) n = 120 and . = 0.98. If the probability is 0.20 that a certain bank will refuse a loan application, use the normal approximation to determine (to three decimals) the probability that the bank will refuse at most 40 of 225 loan applications. If X has a geometric distribution with θ = 1/3 , find the formula for the probability distribution of the random variable Y = 4 – 5X. If the probability density of X is given by And Y = X2, find (a) The distribution function of Y; (b) The probability density of Y. If X1 and X2 are independent random variables having the geometric distribution with the parameter θ, show that Y = X1 + X2 is a random variable having the negative binomial distribution with the parameters θ and k = 2.
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