Question

In studies for a medication, 42% percent of patients gained weight as a side effect. Suppose 50 patients are randomly selected. Can we use the normal approximation to the binomial to approximate the probability that exactly 22 patients will gain weight as a side effect.

If no, explain why.

If yes, what mean and standard deviation do we use and what probability do we calculate? (dont actually calculate).

Answer yes or no and follow up as requested?

Answer 1

Solution:

Given that,

P = 0.42

1 - P = 0.58

n = 50

Here, BIN ( n , P ) that is , BIN (50 , 0.42)

According to normal approximation binomial,

X Normal

Mean = = n*P = 21

Standard deviation = =n*p*(1-p) = 12.18

We using continuity correction factor

P(X = a) = P( a - 0.5 < X < a + 0.5)

P(21.5 < x < 22.5) = P((21.5 - 21)/ 12.18) < (x - ) /  < (22.5 - 21) / 12.18) )

= P(-0.29 < z < 0.43)

= P(z < 0.43) - P(z < -0.29)

= 0.6664 - 0.3859

Probability = 0.2805

Yes.