Suppose we have a binomial experiment in which success is defined to be a partic

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 = 36 and p = 0.24. Can we approximate p by a normal distribution? Why? (Use 2 decimal places.)

yes or no p can or cannot be approximated by a normal random variable because .

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

(b) Suppose n = 25 and p = 0.15. Can we safely approximate p by a normal distribution? Why or why not?
, p be approximated by a normal random variable because .

(c) Suppose n = 57 and p = 0.16. Can we approximate p by a normal distribution? Why? (Use 2 decimal places.)

, p be approximated by a normal random variable because

.

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

Explanation / Answer

a) np = 36 * 0.24 = 8.64

nq = 36 *( 1- 0.24) = 27.36

p = np * p = 6.566

p = sqrt(nq) *p = 3.975

Yes,we approximate p by a normal distribution . because np and nq are greater than 5

b)

np = 25 * 0.15 = 3.75

nq = 25 *( 1- 0.15) = 21.25

p = np * p = 3.187

p = sqrt(nq) *p = 3.918

Yes,we approximate p by a normal distribution

c)

np = 57 * 0.16 = 9.12

nq = 57 *( 1- 0.16) = 47.88

p = np * p = 7.661

p = sqrt(nq) *p = 5.812

Yes,we approximate p by a normal distribution , because np and nq are greater than 5

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