Question

62% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 43 owned dogs are randomly selected, find the probability that

a. Exactly 27 of them are spayed or neutered.
b. At most 26 of them are spayed or neutered.
c. At least 27 of them are spayed or neutered.
d. Between 22 and 27 (including 22 and 27) of them are spayed or neutered.

Round all answers to 4 decimal places.

Answer 1

Solution:

Given:

p = 0.62

n = sample size = 43

a) We have to find P(X=27) = ...?

Using Binomial distribution,

Therefore,

b)

We have to find P(X26) = ...?

Using excel formula:

=BINOMDIST(26,43,0.62,TRUE)

P(X26) = 0.4749

c)

We have to find P(X27) =...?

Using excel formula:

=1-BINOMDIST(26,43,0.62,TRUE)

P(X27) = 0.5251

d) We have to find P() = ...?

Using excel formula,

=BINOMDIST(27,43,0.62,TRUE)-BINOMDIST(21,43,0.62,TRUE)

P() = 0.5452

Done