Respuesta :
Answer:
Yes, the normal curve can be used as an approximation to the binomial probability.
Step-by-step explanation:
Let X = number of students that pass their college placement exam.
The probability that a given student will pass their college placement exam is, P (X) = p = 0.53.
A random sample of n = 127 students is selected.
The random variable X follows a Binomial distribution.
But the sample size is too large.
A Normal approximation to Binomial can be used to approximate the distribution of proportion p.
The conditions to be satisfied are:
- np ≥ 10
- n(1-p) ≥ 10
Check whether the conditions are satisfied as follows:
[tex]np=127\times0.53=67.31>10[/tex]
[tex]n(1-p)=127\times(1-0.53)=59.69>10[/tex]
Both he conditions are satisfied.
Thus, a normal curve can be used as an approximation to the binomial probability.
