Question

Use the normal distribution to approximate the following binomial distribution. A recent survey indicated that 55% of the people in a certain community own a motorcycle. If 35 people from this community are chosen at random, what is the probability that fewer than 23 own a motorcycle?

Answer 1

0.86 (Approx)

Explanation:

Given:

n = 35

P = 55% = 0.55

Q = 1 - p = 0.45

Computation:

Standard deviation σ = √npq

Standard deviation σ = √(35)(.55)(.45)

Standard deviation σ = 2.9432

Mean μ = np = 35 x 0.55 = 19.25

p[(x-np)/ σ ]

P[z<1.04204]

= 0.86 (Approx)