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Part a)
It was given that 3% of patients gained weight as a side effect.
This means
The mean is
The standard deviation is
We want to find the probability that exactly 24 patients will gain weight as side effect.
P(X=24)
We apply the Continuity Correction Factor(CCF)
P(24-0.5<X<24+0.5)=P(23.5<X<24.5)
We convert to z-scores.
Part b) We want to find the probability that 24 or fewer patients will gain weight as a side effect.
P(X≤24)
We apply the continuity correction factor to get;
P(X<24+0.5)=P(X<24.5)
We convert to z-scores to get:
Part c)
We want to find the probability that
11 or more patients will gain weight as a side effect.
P(X≥11)
Apply correction factor to get:
P(X>11-0.5)=P(X>10.5)
We convert to z-scores:
Part d)
We want to find the probability that:
between 24 and 28, inclusive, will gain weight as a side effect.
P(24≤X≤28)=
P(23.5≤X≤28.5)
Convert to z-scores: