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 24 have satellite television?

a) 0.9332

b) 0.8980

c) 0.9525

d) 0.9463

e) 0.9251

f) None of the above.

Answer 1

Solution :

Using binomial distribution,

= n * p = 0.55 * 35 = 19.25

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

Using continuity correction ,

= P((x - ) / < (23.5 - 19.25) / 2.9432)

= P(z < 1.44)

= 0.9251

Probability = 0.9251

e)