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Answer:
0.9466 = 94.66% probability that the weight of a randomly selected steer is between 639 and 1420lbs.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Find the probability that the weight of a randomly selected steer is between 639 and 1420lbs.
This is the pvalue of Z when X = 1420 subtracted by the pvalue of Z when X = 639. So
X = 1420
has a pvalue of 0.9821
X = 639
has a pvalue of 0.0355
0.9821 - 0.0355 = 0.9466
0.9466 = 94.66% probability that the weight of a randomly selected steer is between 639 and 1420lbs.