Question

Keith is a drummer who purchases his drumsticks online. When practicing with the newest pair, he notices they feel heavier than usual. When he weighs one of the sticks, he finds that it is 1.87 oz. The manufacturer's website states that the average weight of each stick is 1.50 oz with a standard deviation of 0.15 oz. Assume that the weight of the drumsticks is normally distributed. What is the probability of the stick's weight being 1.87 oz or greater? Give your answer as a percentage precise to at least two decimal places. You might find this table of standard normal critical values useful.

Answer 1

we have

we have to find the probability that stick's weight being 1.87oz or greater

Using the formula

x = 1.87, setting the given values, we get

this gives us

using the identity

we can write

using z distribution table, looking 2.0 in the left column and 0.47 in the top most row, then selecting the intersecting cell, we get

converting to percentage, 0.0068*100 = 0.68%

So, required percentage is 0.68%