Question

Use the normal distribution to approximate the following binomial distribution. A recent survey indicated that 55% of the people in a certain town have satellite television. If 35 people from this town are chosen at random, what is the probability that fewer than 21 have satellite television?

a-0.6915

b-0.6628

c-0.7486

d-0.7224

e-0.5987

Answer 1

Solution :

Using binomial distribution,

= n * p = 35 * 0.55 = 19.25

= n * p * q = 35 * 0.55 * 0.45 = 2.9432

Using continuity correction ,

= P((x - ) / < (20.5 - 19.25) / 2.9432)

= P(z < 0.42)

= 0.6628

Probability = 0.6628

b)