Question

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(a) Suppose n = 43 and p = 0.23. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np =

nq =

, p̂ be approximated by a normal random variable because .

What are the values of μp̂ and σp̂? (Use 3 decimal places.)

μp̂ =

σp̂ =

Answer 1

Solution:

Given ,

n = 43 and p = 0.23

q = 1 - p = 1 - 0.23 = 0.77

np = 43 * 0.23 = 9.89

nq = 43 * 0.77 = 33.11

np = 9.89

nq = 33.11

No , p̂ cannot be approximated by a normal random variable because np < 10.

What are the values of μp̂ and σp̂?

=  p = 0.23

  =     

=  

=  0.064

= 0.23

= 0.064