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Answer :
The probability that a quart of this brand of milk chosen at random will contain between 31 and 359 grams of butterfat is approximately 1.
To find the probability of the butterfat content being between 31 and 359 grams, we first need to calculate the z-scores for these values.
The z-score formula is:
z = (x - μ) / σ
where:
x = value we want to find the probability for (31 or 359)
μ = mean of the butterfat content (319 grams)
σ = standard deviation of the butterfat content (4 grams)
For 31 grams of butterfat:
z = (31 - 319) / 4 = -87
For 359 grams of butterfat:
z = (359 - 319) / 4 = 10
Since the z-scores are very large, we can approximate that the probability is 1, meaning it is highly likely that a quart of this brand of milk chosen at random will contain between 31 and 359 grams of butterfat.
(bi)
To find the probability of the butterfat content being between 29 and 319 grams, we again need to calculate the z-scores for these values.
For 29 grams of butterfat:
z = (29 - 319) / 4 = -72.5
For 319 grams of butterfat:
z = (319 - 319) / 4 = 0
Using the standard normal distribution table or a calculator, the probability associated with these z-scores is approximately 0.5000.
To know more about Probability, visit:
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