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Answer :
The question deals with computing probabilities for different values in a normal distribution of the compressive strength of concrete. This requires calculation of z-scores and the use of a z-table or statistical software to find probabilities for the specified values given the mean and standard deviation.
Specifically Statistics, as it deals with calculations related to normal distribution, mean, and standard deviation. This problem involves calculating probabilities based on certain values in a normal distribution.
Assuming the 'pa' and 'psa' in your question are typographical errors and you actually mean 'psi', we can represent any value 'X' on this normal distribution using the standard score or 'z-score' formula:
Z = (X - μ) / σ
Where 'μ' is the mean, 'σ' is the standard deviation, and 'X' is the actual value you want to compute probability for.
For (a), we want to know the probability that the compressive strength is less than 2700 psi. So, X = 2700, μ = 3000, and σ = 300. Plug these values into the formula to find the z-score, and then look that z-score up in a z-table to find the probability.
The same principles apply for (b) and (c). Compute the 'z-scores', then use a z-table or statistical software to find the probabilities.
Learn more about the topic of Normal Distribution here:
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