Question

Suppose that Y has a binomial distribution with

p = 0.60.

(a)

Use technology and the normal approximation to the binomial distribution to compute the exact and approximate values of

P(Y ≤ μ + 1)

for n = 5, 10, 15, and 20. For each sample size, pay attention to the shapes of the binomial histograms and to how close the approximations are to the exact binomial probabilities. (Round your answers to five decimal places.)

n = 5

exact value

P(Y ≤ μ + 1)

= approximate value

P(Y ≤ μ + 1)

≈

n = 10

exact value

P(Y ≤ μ + 1)

= approximate value

P(Y ≤ μ + 1)

≈

n = 15

exact value

P(Y ≤ μ + 1)

= approximate value

P(Y ≤ μ + 1)

≈

n = 20

exact value

P(Y ≤ μ + 1)

= approximate value

P(Y ≤ μ + 1)

≈

Answer 1

For each n,

the exact values are calculated in excel using the formula:

= BINOMDIST(np+1,n,p,TRUE) , where n, p and np are according to the values given.

the approximate values are calculated in excel using the formula:

=NORMDIST(np+1,np,npq,TRUE), where np and npq are selected in accordance.

p=	0.6
n=	5	10	15	20
np=	3	6	9	12
npq=	1.2	2.4	3.6	4.8
Exact value=	0.92224	0.83271	0.782722	0.749989
Approximate value =	0.797672	0.661539	0.609409	0.582516