In studies for a medication, 3 percent of patients gained weight as a side effect. Suppose 643 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that
(a) exactly 24 patients will gain weight as a side effect.
(b) 24 or fewer patients will gain weight as a side effect.
(c) 11 or more patients will gain weight as a side effect.
(d) between 24 and 28, inclusive, will gain weight as a side effect.

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:

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step-by-step explanation:

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