Use the normal distribution to approximate the following binomial distribution. A recent survey indicated that 55% of the people

Question

3 years ago

6

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?

Mathematics

1 answer:

madam [21] · Answer 1 · 2022-04-24T04:05:07+03:00

madam [21]3 years ago

7 0

Answer:

0.86 (Approx)

Step-by-step 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)