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 2.33 oz. The manufacturer's website states that the average weight of each stick is 1.75 oz with a standard deviation of 0.22 oz. Assume that the weight of the drumsticks is normally distributed. What is the probability of the stick's weight being 2.33 oz or greater? Give your answer as a percentage precise to at least two decimal places.

Question

Mathematics

Anton

27 September, 02:46

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 2.33 oz. The manufacturer's website states that the average weight of each stick is 1.75 oz with a standard deviation of 0.22 oz. Assume that the weight of the drumsticks is normally distributed. What is the probability of the stick's weight being 2.33 oz or greater? Give your answer as a percentage precise to at least two decimal places.

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Serena Ochoa · Answer 1

The probability of the stick's weight being 2.33 oz or greater is 0.41%.

Step-by-step explanation:

Test statistic (z) = (weight - mean) / sd

weight of stick = 2.33 oz

mean = 1.75 oz

sd = 0.22 oz

z = (2.33 - 1.75) / 0.22 = 2.64

The cumulative area of the test statistic is the probability that the weight is 2.33 oz or less. The cumulative area is 0.9959.

The probability the weight is 2.33 or greater = 1 - 0.9959 = 0.0041 = 0.41%