Question

g According to Major League Baseball rules, a baseball should weigh between 5 and 5.25 ounces and have a circumference of between 9 and 9.25 inches. Suppose the weight of a baseball (in ounces) has a uniform distribution with a 5 5.085 and b 5 5.155, and the circumference (in inches) has a uniform distribution with a 5 9.0 and b 5 9.1. a. Find the probability that a randomly selected baseball has a weight greater than 5.14 ounces. Write a Solution Trail for this problem. b. Find the probability that a randomly selected baseball has a circumference less than 9.03 inches. c. Suppose the weight and the circumference are independent. Find the probability that a randomly selected baseball will have a weight between 5.11 and 5.13 ounces and a circumference between 9.04 and 9.06 inches.

Answer 1

a) e probability that a randomly selected baseball has a weight greater than 5.14 ounces

=P(X>5.14) =(b-x)/(b-a) =(5.155-5.14)/(5.155-5.085)=0.2143

b)

probability that a randomly selected baseball has a circumference less than 9.03 inches

=P(X<9.03) =(x-a)/(b-a) =(9.03-9)/(9.1-9)=0.3

c) probability that a randomly selected baseball will have a weight between 5.11 and 5.13 ounces and a circumference between 9.04 and 9.06 inches

=((5.13-5.11)/(5.155-5.085))*((9.06-9.04)/(9.1-9.0))=0.0571