In studies for a medication, 12 percent of patients gained weight as a side effe

Question

In studies for a medication, 12 percent of patients gained weight as a side effect. Suppose 707 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that (a) exactly 85 patients will gain weight as a side effect. (b) no more than 85 patients will gain weight as a-side effect. (c) at least 99 patients will gain weight as a side effect. What does this result suggest? Click here to view the standard normal distribution table (page 1 Click here to view the standard normal distribution table (page 2) i Standard Normal Distribution Table (pade 1) (a) P(85) = (Round to four decimal places as needed) -34 -3.3 -3.2 -3.1 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.000 00010 00009 0.0009 0.0009 00008 00008 00008 00008 Enter your answer in the answer box and then click Check Answer. Print Done remaining

Explanation / Answer

here mean =np =707*0.12=84.84

std deviation=(np(1-p))1/2 =8.641

a) P(X=85)=P(84.5<X<85.5) =P((84.5-84.84)/8.641<Z<(85.5-84.84)/8.641)=P(-0.0393<Z<0.0764)=0.5304-0.4843

=0.0461

b) P(X<=85)=P(Z<(85.5-84.84)/8.641)=P(Z<0.0764)=0.5304

c)P(X>=99)=1-P(X<=98)=1-P(Z<(98.5-84.84)/8.641)=1-P(Z<1.5809) =1-0.9431 =0.0569

above event is not unsuual as its probability is greater then 0.05

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