Slow pitch baseball, mean:28 and standard deviation:2.1. Wooden baseball, mean:33 and standard deviation:3.2. Find probability that a slow pitch softball bat weighs more than a wooden baseball bat?

Question

The distribution of the weights of slow pitch softball bats and wooden baseball bats are each approximately normal.

Answer 1

First, we are assuming the question is actuallly "Find the probability that a randomly selected slow pitch softball bat will weigh more than a randomly selected wooden baseball bat"

You are trying to determine the distribution of the difference between two random variables. Since a difference between two normally distributed variables is also normally distributed we find that the mean of Ww - Wsp is going to be 33-28 , or 5. This is the average expected difference between the wooden bat and the slow pitch bat. The variance of the Diference is equal the the sum of the two variances of the independent variables . This is 4.41+10.24 or 14.65 (Variance) or 3.828 for standard deviation.

Calculating the probability that the difference between the wood and slow pitch bat is LESS than zero (ie Ww - Wsp <0 or Wsp > Ww) is a matter of using normal distribution probabilty tables for a difference of less than or equal to 0 when mean difference is 5 and with a sd of 3.828

P(Wsp > Ww) = 0.09575