Answer to Question #320780 in Statistics and Probability for Struggling

Question

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 [1]

ii. What is the probability distribution? State the values of the parameters [2]

iii. Justifying the suitability of the probability distribution identified in part (ii) [4]

iv. Calculate the probability that at most 2 bottles do not meet the company’s Standards [4]

v. The expected number of bottles that do not meet the company’s standards. [2]

vi. The amount of sodium sulfate, in mg, found in the bottled water follows a normal distribution with a mean 13mg and a standard deviation of 2.5mg. It is known that 76% of the bottles have a mean that is more than x mg. Find the value of x