b) A bottled water company has found in the past that 2% of their bottled water does not meet the company’s high standards. As such periodic samples are taken and tested for their quality. If from the last batch a sample of 12 bottles are taken and tested, determine the probability: i. Carefully defining the random variable of interest ii. What is the probability distribution? State the values of the parameters iii. Justifying the suitability of the probability distribution identified in part (ii) iv. Calculate the probability that at most 2 bottles do not meet the company’s Standards v. The expected number of bottles that do not meet the company’s standards.
b) A bottled water company has found in the past that 2% of their bottled water does not
meet the company’s high standards. As such periodic samples are taken and tested for
their quality. If from the last batch a sample of 12 bottles are taken and tested, determine
the probability:
i. Carefully defining the random variable of interest
ii. What is the probability distribution? State the values of the parameters
iii. Justifying the suitability of the probability distribution identified in part (ii)
iv. Calculate the probability that at most 2 bottles do not meet the company’s
Standards
v. The expected number of bottles that do not meet the company’s standards.
c) The amount of sodium sulfate, in mg, found in the bottled water follows a
distribution
of the bottles have a mean that is more than x mg. Find the value of x.
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