Question

In studies for a? medication, 77 percent of patients gained weight as a side effect. Suppose 513 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that

?(a) exactly 20 patients will gain weight as a side effect.

?(b) 20 or fewer patients will gain weight as a side effect.

?(c) 42 or more patients will gain weight as a side effect.

?(d) between 20 and 50?, ?inclusive, will gain weight as a side effect.

Answer 1

Here, we are given the distribution as:

This can be approximated to a normal distribution as:

a) The required probability here is computed as:

Applying continuity correction, we get:

Converting this to a standard normal variable, we get:

As the z values in the above case are very very high, the above probability is approximately equal to 0

Therefore 0 is the required probability here.

b) The probability here is computed as:

Applying the continuity correction, we get:

Converting this to a standard normal variable, we get:

Again the z score here is very large, and so approximately probability is 0

Therefore 0 is the required probability here.

c) The required probability here is computed as:

Applying the continuity correction factor, we get:

Converting this to a standard normal variable, we get:

As the z value here is very very low, therefore the approximate probability above would be 1

Therefore 1 is the required probability here.

b) Again using the same method as above, we have here:

P( 20 <= X <= 50 )

Again as the z scores would be very very low, the approximate probability here would be 0

Therefore 0 is the required probability here.