The weights of steers in a herd are distributed normally. The standard deviation is 200lbs and the mean steer weight is 1000 lbs. Find the probability that the weight of a randomly selected steer is between 639 and 1420lbs. Round your answer to four decimal places.

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.

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