Question

Rod 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 2.66 oz. The manufacturer's website states that the average weight of each stick is 2.25 oz with a standard deviation of 0.17 oz. Assume that the weight of the drumsticks is normally distributed.What is the probability of the stick's weight being 2.66 oz or greater

Answer 1

Answer: 0.0080

Step-by-step explanation:

Given : The manufacturer's website states that the average weight of each stick is $\mu=2.25$ oz with a standard deviation of $\sigma=0.17$ oz.

We assume the weight of the drumsticks is normally distributed.

Using formula $z=\dfrac{x-\mu}{\sigma}$, the z-value corresponds x=2.66 will be :-

$z=\dfrac{2.66-2.25}{0.17}\approx2.41$

By using the standard normal distribution table for z, we get

P-value = $P(z\geq2.41)=1-P(z<2.41)$

$\\\\=1-0.9920237=0.0079763\approx0.0080$

Hence, the probability of the stick's weight being 2.66 oz or greater=0.0080