Answer :
Final answer:
To find the proportion of steer weighing between 1100 and 1200 pounds in this normal distribution, calculate the individual z-scores of both weights, then find the areas corresponding to these z-scores in a standard normal distribution table. Subtract the area of the smaller z-score from the larger one to get the requested proportion.
Explanation:
The question you're asking is about the application of normal distribution in statistics, particularly in determining the proportion of steer that weigh between certain values. This kind of calculation can be done using a z-score, which measures how many standard deviations an element is from the mean. In this case, the mean is 1152 pounds, the standard deviation is 84 pounds and you're looking for the proportion between 1100 and 1200 pounds.
Firstly, let's calculate the z-score for 1100 pounds: (1100 - Mean) / Standard Deviation = (1100 - 1152) / 84 = -0.619.
Then, we'll calculate the z-score for 1200 pounds: (1200 - Mean) / Standard Deviation = (1200 - 1152) / 84 = 0.571.
To find the proportion between these two values, you'll need to use a standard normal distribution table or a similar tool. Remember that the area under the curve in a normal distribution represents the probability or proportion. So, you'll identify the areas corresponding to both z-scores and then subtract the smaller area (for -0.619) from the larger area (for 0.571) to obtain the proportion of steer that weigh between 1100 and 1200 pounds.
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