Answers:
1) no, 57 is not considered a significantly high number of girls;
2) the probability to be used is p (x ≥ 57)
We are given the following:
n = 100
p (x = 57) = probability of getting exactly 57 girls = 0.03
p (x ≥ 57) = probability of getting at least 57 girls = 0.097
This is a problem of normal approximation to a binomial distribution.
The distribution of the probabilities can be approximated to a normal distribution centered at the mean probability (x = 50).
In order to say if 57 is a significanty high number of girls, we need to consider what is the probability of getting more than 57 girls, which means that we need to consider at what point of the distribution is 57.
Therefore, we need to consider the area on the right of 57: how big it is?
The answer to this question is given by the probability of getting at least 57 girls: p (x ≥ 57).
The problem states that to consider a number of girls to be significantly high, the probability must be ≤ 0.05; we know
p (x ≥ 57) = 0.097 > 0.05
Hence, 57 can not be considered a significantly high number of girls.
