Answer:
Yes, the normal curve can be used as an approximation to the binomial probability.
Step-by-step explanation:
Let <em>X</em> = number of students that pass their college placement exam.
The probability that a given student will pass their college placement exam is, P (X) = <em>p</em> = 0.53.
A random sample of <em>n</em> = 127 students is selected.
The random variable <em>X</em> 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 <em>p</em>.
The conditions to be satisfied are:
- <em>np</em> ≥ 10
- <em>n</em>(1-<em>p</em>) ≥ 10
Check whether the conditions are satisfied as follows:
Both he conditions are satisfied.
Thus, a normal curve can be used as an approximation to the binomial probability.