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 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.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 2E
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Answer part b section iv and v, as well answer part c

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:
Carefully defining the random variable of interest
What is the probability distribution? State the values of the parameters
Justifying the suitability of the probability distribution identified in part (ii,
i.
ii.
iii.
Calculate the probability that at most 2 bottles do not meet the company's
Standards
iv.
The expected number of bottles that do not meet the company's standards.
V.
c) 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.
Transcribed Image Text: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: Carefully defining the random variable of interest What is the probability distribution? State the values of the parameters Justifying the suitability of the probability distribution identified in part (ii, i. ii. iii. Calculate the probability that at most 2 bottles do not meet the company's Standards iv. The expected number of bottles that do not meet the company's standards. V. c) 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.
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