The weights of steers in a herd are distributed normally. The standard deviation is 200lbs and the mean steer weight is 1000lbs. Find the probability that the weight of a randomly selected steer is between 720 and 1160 lbs. Round your answer to four decimal places.
Here, μ = 1000, σ = 200, x1 = 720 and x2 = 1160. We need to compute P(720<= X <= 1160). The corresponding z-value is calculated using Central Limit Theorem
z = (x - μ)/σ
z1 = (720 - 1000)/200 = -1.4
z2 = (1160 - 1000)/200 = 0.8
Therefore, we get
P(720 <= X <= 1160) = P((1160 - 1000)/200) <= z <=
(1160 - 1000)/200)
= P(-1.4 <= z <= 0.8) = P(z <= 0.8) - P(z <=
-1.4)
= 0.7881 - 0.0808
= 0.7073
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