Let r = radius of the hard rubber ball. The circumference of the ball is 13 inches, therefore 2πr = 13 r = 13/(2π) = 2.069 inches The diameter of the ball is 2*2.069 = 4.138 inches.
The ball is hard and cannot be compressed. Therefore the length of a side of the smallest cube-shaped box with integer dimensions is 5 inches. The volume of the box is 5³ = 125 in³.
Binomial distribution can be used because the situation satisfies all the following conditions:1. Number of trials is known and remains constant (n)2. Each trial is Bernoulli (i.e. exactly two possible outcomes) (success/failure)3. Probability is known and remains constant throughout the trials (p)4. All trials are random and independent of the othersThe number of successes, x, is then given bywhere Here we're given p=0.10 [ success = defective ] n=3