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11.Please provide solutions to the following Questions and show all necessary wo

ID: 2924954 • Letter: 1

Question

11.Please provide solutions to the following Questions and show all necessary work. Feel free to use any statistical software like R.

11. A standard drug is known to be effective in 80% of the cases in which it is used. A new drug is is (a) If the new and old drugs were equally effective (i.e. the probabilities of them being effective on a randomly chosen case were equal), what is the probability of the new drug being effective in 84 or more cases? (b) The new drug was found to be effective in 84 cases. Based on the probability obtained above, would you conclude that the new drug is superior?

Explanation / Answer

NORMAL APPROXIMATION TO BINOMIAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
mean ( np ) = 100 * 0.8 = 80
standard deviation ( npq )= 100*0.8*0.2 = 4
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
a.
P(X < 84) = (84-80)/4
= 4/4= 1
= P ( Z <1) From Standard NOrmal Table
= 0.8413
P(X > = 84) = (1 - P(X < 84))
= 1 - 0.8413 = 0.1587

b.
it is effective only about to 15% of the cases and which is very minimal and not advisible