Answer :
Final answer:
The z-score of a 9-kilo blow is -3.06 based on the given mean and standard deviation of the force required to puncture a cardboard mailing tube. However, the probability of a tube puncturing under this force is close to 0.
Explanation:
To find the probability that a tube will puncture if its struck with a 9-kilo blow, we need to use z-scores in statistics. The z-score is a statistical measurement that describes a value's relationship to the mean of a group of values.
A z-score is computed from the raw score using the following formula: Z = (X - μ) / σ; where Z is the z-score, X is the value being calculated, μ is the mean, and σ is the standard deviation.
In our case, we can plug in the given values into this formula: Z = (9 - 14.5) / 1.8 = -3.06. Once we have the z-score, we need to look it up in a standard normal distribution table or use a statistical calculator/online tool to find the area to the left of -3.06, which gives us the probability. However, typically, z-tables or calculators will not compute values this extreme. One can safely assume that the probability is extremely close to 0 that a tube will puncture when struck with a 9-kilo blow.
Learn more about Probability here:
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