For a binomial experiment in which success is defined to be a particular quality or attribute that interests us, with n=36 and p as 0.23, we can approximate p hat by a normal distribution.
Since n=36 , p=0.23 , thus q= 1-p = 1-0.23=0.77
therefore,
n*p= 36*0.23 =8.28>5
n*q = 36*0.77=27.22>5
and therefore, p hat can be approximated by a normal random variable, because n*p>5 and n*q>5.
The question is incomplete, a possible complete question is:
Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
Suppose n = 36 and p = 0.23. Can we approximate p hat by a normal distribution? Why? (Use 2 decimal places.)
n*p = ?
n*q = ?
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