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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
 #1
avatar+6046 
+1

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
 #2
avatar+34 
+1

Thank you! 

RandiLaine98  Apr 22, 2019

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