Question

The weights of steers in a herd are distributed normally. the standard deviation is 200 lbs and the mean steer weight is 1300 lbs. find the probability that the weight of a randomly selected steer is between 1000 and 1437 lbs. round your answer to four decimal places.

Answer 1

Given a mean = 1300 and a Ď = 200, we can calculate that the lower bound of 1000 is (1000 - 1300) / 200 = -1.5 standard deviations below the mean. The upper bound is (1437 - 1300) / 200 = 0.685 standard deviations from the mean. Using the cumulative distribution function, we can calculate that the probability a randomly chosen steer lies on the interval [1000, 1437] is CDF(0.685) - CDF(-1.5) = 0.68652083824480004 p = 0.6865