# A vending machine automatically pours soft drinks into cups.

A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into acup is normally distributed with a mean of 7.6 ounces and standard deviation of 0.4 ounce. Examine thefigure below and answer the following questions.(a) Estimate the probability that the machine will overflow an 8-ounce cup. (Round your answer to twodecimal places.)(b) Estimate the probability that the machine will not overflow an 8-ounce cup. (Round your answer totwo decimal places.)(c) The machine has just been loaded with 884 cups. How many of these do you expect will overflowwhen served?cupsSuppose x has a distribution with ? = 63 and ? = 15.(a) If random samples of size n = 16 are selected, can we say anything about the x distribution ofsample means?Yes, the x distribution is normal with mean ? x = 63 and ? x = 0.9.Yes, the x distribution is normal with mean ? x = 63 and ? x = 3.75.No, the sample size is too small.Yes, the x distribution is normal with mean ? x = 63 and ? x = 15.(b) If the original x distribution is normal, can we say anything about the x distribution of randomsamples of size 16?Yes, the x distribution is normal with mean ? x = 63 and ? x = 0.9.No, the sample size is too small.Yes, the x distribution is normal with mean ? x = 63 and ? x = 15.Yes, the x distribution is normal with mean ? x = 63 and ? x = 3.75.Find P(59 ? x ? 64). (Round your answer to four decimal places.)

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