Answer:
The minimum sample size needed for use of the normal approximation is 50.
Step-by-step explanation:
Suitability of the normal distribution:
In a binomial distribution with parameters n and p, the normal approximation is suitable is:
np >= 5
n(1-p) >= 5
In this question, we have that:
p = 0.9
Since p > 0.5, it means that np > n(1-p). So we have that:
[tex]n(1-p) \geq 5[/tex]
[tex]n(1 - 0.9) \geq 5[/tex]
[tex]0.1n \geq 5[/tex]
[tex]n \geq \frac{5}{0.1}[/tex]
[tex]n \geq 50[/tex]
The minimum sample size needed for use of the normal approximation is 50.