+34 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
+6250 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)
