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2standard deviation a particular telephone number is used to receive both voice calls and fax messages. suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. (a) what is the expected number of calls among the 25 that involve a fax message?

For a multistate lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities. complete parts (a) through (c) below. x (cash prize, $) p(x) grand prizegrand prize 0.000000008860.00000000886 200,000 0.000000390.00000039 10,000 0.0000016950.000001695 100 0.0001582930.000158293 7 0.0039114060.003911406 4 0.0080465690.008046569 3 0.012865710.01286571 0 0.975015928140.97501592814 (a) if the grand prize is $13 comma 000 comma 00013,000,000, find and interpret the expected cash prize. if a ticket costs $1, what is your expected profit from one ticket? the expected cash prize is $nothing.

Manipulation manufacturing's (amm) standards anticipate that there will be 5 pounds of raw material used for every unit of finished goods produced. amm began the month of maymay with 8,000 pounds of raw material, purchased 25,500 pounds for $ 15,300 and ended the month with 7,400 pounds on hand. the company produced 4,9004,900 units of finished goods. the company estimates standard costs at $ 1.10 per pound. the materials price and efficiency variances for the month of maymay were: