Question

According to Major League Baseball (MLB) rules, the baseball used during games must weigh between 5 and 5.25 ounces. If a factory produces baseballs whose weights are approximately normally distributed with a mean of 5.11 ounces and standard deviation 0.062 ounces, find the probability that a randomly selected baseball

a) will weigh between 5 and 5.2 ounces.

b) is too heavy to be used by MLB.

c) will be able to be used by MLB.

If an order of 10,000 baseballs is placed, about how many are able to be used by MLB?

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	5.11
std deviation   =σ=	0.062

a)

probability =P(5<X<5.2)=P((5-5.11)/0.062)<Z<(5.2-5.11)/0.062)=P(-1.77<Z<1.45)=0.9265-0.0384=0.8881

b)

probability =P(X>5.25)=P(Z>(5.25-5.11)/0.062)=P(Z>2.26)=1-P(Z<2.26)=1-0.9881=0.0119

c)

probability =P(5<X<5.25)=P((5-5.11)/0.062)<Z<(5.25-5.11)/0.062)=P(-1.77<Z<2.26)=0.9881-0.0384=0.9497

number of balls to be used =np=10000*0.9497 =9497