Question

The probability of flu symptoms for a person not receiving any treatment is 0.037. In a clinical trial of a common drug used to lower​ cholesterol, 39 of 983 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu​ symptoms, estimate the probability that at least 39 people experience flu symptoms. What do these results suggest about flu symptoms as an adverse reaction to the​ drug?

Answer 1

Answer:

X ~ Bin(n,p)

Where n = 983 , p = 0.037

Mean = np = 983 * 0.037 = 36.371

Standard deviation = sqrt (np(1-p))

= sqrt ( 983* 0.037 ( 1 - 0.037) )

= 5.9182

Using normal approximation,

P(X < x) = P(Z < ( x - Mean ) / SD)

With continuity correction ,

P(X >= 39) = P(Z > (38.5 - 36.371) / 5.9182)

= P(Z > 0.35)

= 1-P(Z<0.35)

=1 - 0.6368

= 0.3632

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