suppose that 1 out of 10 plasma televisions shipped with a defective speaker.

out of a shipment of n=400 plasma televisions. find the probability that there are
a) at most 40 with defective speakers (Hint: Use the dishonest- coin principle with P= 1/10=0.1 to the find the mean and standard deviation. 
B) Most than 52 with defective speakers

 Apr 22, 2019

It seems that the dishonest coin principle is the fact that the Central Limit theorem states that

given enough samples the outcome a set of Bernoulli trials as described in the problem

is approximately normally distributed with parameters


\(\mu = n p\\ \sigma = n p (1-p)\\ \text{Where }p \text{ is the probability of the success of a single event}\)


\(\text{In this problem }n=400,~p=\dfrac{1}{10}\\ \mu = 40\\ \sigma = \sqrt{(400)(0.1)(0.9)} =6\)


\(\text{Denoting the CDF of the standard normal as }\Phi(x) \text{ we have}\\ P[n\leq 40] = \Phi\left(\dfrac{40-40}{6}\right) = \Phi(0) = \dfrac 1 2\)


Now just apply this same principle to (B)

 Apr 22, 2019

Thank you! 

RandiLaine98  Apr 22, 2019

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