Question

Suppose a drug is known to have mild side effects in 75% of the people who take it . It is administered to 100 people. Using both the binomial distribution and the normal approximation, you have calculated the probability that more than 70 people will experience mild side effects. Based on your answers to the previous questions, choose all that apply.

i. Since our experimental conditions satisfy the requirements for its use, the estimate from the normal approximation is appropriate as long as we do not require a high degree of accuracy

ii. Binomial is more accurate than the normal approximation, however, binomial is computationally more expensive ( it requires R) where the normal approximation can be done using tables.

iii. It does not make sense to use the normal approximate because our sample is not large enough.

iii. none of the above

Answer 1

Correct options:

i. Since our experimental conditions satisfy the requirements for its use, the estimate from the normal approximation is appropriate as long as we do not require a high degree of accuracy

ii. Binomial is more accurate than the normal approximation, however, binomial is computationally more expensive ( it requires R) where the normal approximation can be done using tables.

Explanation:

Conditions for normal approximation to binomial distribution are satisfied as shown below:

Condition 1:

10% Condition: Since the population is very large, the sample size n = 100 is no morethan 10% of populaton.

Condition 2:

n = 100

p = 0.75

So,

np = 100 X 0.75 = 75 10.

So, this condition is satisfied.

Condition 3:

n = 100

p = 0.75

So,

n(1-p) = 100 X 0.25 = 25 10.

So, this condition is satisfied.

So, since our experimental conditions satisfy the requirements for its use, the estimate from the normal approximation is appropriate as long as we do not require a high degree of accuracy.

Further, Binomial is more accurate than the normal approximation, however, binomial is computationally more expensive ( it requires R) where the normal approximation can be done using tables.