(a) Two broths, Omar and Ahmad own and operate a small restaurant. Omar washes 40% of...

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(a) Two broths, Omar and Ahmad own and operate a small restaurant. Omar washes 40% of the dishes and Ahmad washes 60% of the dishes using the washing machine. When Omar washes a dish, he might break it with a probability 10%. On the other hand, when Ahmad washes a dish, he might break it with a probability 3%. i. Find the probability that a dish will be broken during washing? ii. If a broken dish was found in the washing machine, find the probability that it was handled by Omar? (b) The formula P(Y = 3) = 33e-3 3! was used to compute a probability from a probability distribution. i. What is the standard deviation of this probability distribution? ii. Find P(Y2), P(Y < 2) and P(Y > 3) to three decimal places, using the fact that e = 0.050 to three decimal places. (c) A charity believes that when it puts out an appeal for charitable donations, the donations it receives will be normally distributed with a mean of $48 and variance of $16. i. Find the probability that a donation will be between $50 and $60. ii. Find the value x such that 10% of donations are more than $x. (a) Two broths, Omar and Ahmad own and operate a small restaurant. Omar washes 40% of the dishes and Ahmad washes 60% of the dishes using the washing machine. When Omar washes a dish, he might break it with a probability 10%. On the other hand, when Ahmad washes a dish, he might break it with a probability 3%. i. Find the probability that a dish will be broken during washing? ii. If a broken dish was found in the washing machine, find the probability that it was handled by Omar? (b) The formula P(Y = 3) = 33e-3 3! was used to compute a probability from a probability distribution. i. What is the standard deviation of this probability distribution? ii. Find P(Y2), P(Y < 2) and P(Y > 3) to three decimal places, using the fact that e = 0.050 to three decimal places. (c) A charity believes that when it puts out an appeal for charitable donations, the donations it receives will be normally distributed with a mean of $48 and variance of $16. i. Find the probability that a donation will be between $50 and $60. ii. Find the value x such that 10% of donations are more than $x.