# Question

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 Questions

Check 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.Post your question

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