Question

In a certain​ area, 34​% of people own a dog. Complete parts a and b below.

a. Find the probability that exactly 8 out of 20 randomly selected people in the area own a dog.

​(Type an integer or decimal rounded to three decimal places as​ needed.)

b. In a random sample of 20 people from this​ area, find the probability that

8 or fewer own a dog. _________

​(Type an integer or decimal rounded to three decimal places as​ needed.)

Answer 1

We have percentage of people own a dog = p = 0.34

20 people are randomly selected. n = 20

Let x denote number of people own a dog.

This follows Binomial distribution.

p( X = x) = nCx * px * ( 1 - p)n-x

a) Here we need to find, probability that exactly 8 people own a dog.

i.e. p ( x = 8)

= 20C8 * 0.348 * ( 1 - 0.34 )20-8

= 125970 * 0.000179 * 0.006832

= 0.154

b) We need to find, probability that 8 or fewer own a dog.

p( x 8 )

= p ( x = 0) + p( x = 1) + p( x =2 ) + p( x = 3 ) + p ( x = 4 ) + p ( x = 5 ) + p ( x = 6 ) + p ( x =7 ) + p ( x =8 )

= 20C0 * 0.340 * ( 1 - 0.34 )20-0 + 20C1 * 0.341 * ( 1 - 0.34 )20-1   + 20C2 * 0.342 * ( 1 - 0.34 )20-2  + 20C3 * 0.343 * ( 1 - 0.34 )20-3  + 20C4 * 0.344 * ( 1 - 0.34 )20-4  + 20C5 * 0.345 * ( 1 - 0.34 )20-5  + 20C6 * 0.346 * ( 1 - 0.34 )20-6  +

20C7 * 0.347 * ( 1 - 0.34 )20-7 + 20C8 * 0.348 * ( 1 - 0.34 )20-8

= 0.000246 + 0.002534+ 0.012402 + 0.038334 + 0.083929 + 0.138356 + 0.178186 + 0.183585 + 0.153683

= 0.791255

0.791