Question

for a certain dog breed, the number of puppies in a litter typically varies from 2 to 6. the following table shows the probability distribution of the random variable ( n ), where ( n ) represents the number of puppies in a litter. also shown are the squared deviations, or distances, from the expected value of 4.5 for the distribution.

number of puppies	2	3	4	5	6
probability	0.05	0.15	0.25	0.35	0.20

what is the variance of the distribution?

Explanation:

Step1: Recall variance formula

Variance is the sum of (squared deviation × probability) for all values of \(N\).

Step2: Calculate each term

For \(N=2\): \(6.25 \times 0.05 = 0.3125\)
For \(N=3\): \(2.25 \times 0.15 = 0.3375\)
For \(N=4\): \(0.25 \times 0.25 = 0.0625\)
For \(N=5\): \(0.25 \times 0.35 = 0.0875\)
For \(N=6\): \(2.25 \times 0.20 = 0.45\)

Step3: Sum all calculated terms

\(0.3125 + 0.3375 + 0.0625 + 0.0875 + 0.45\)

Answer:

1.25