Answer :
The normal distribution is solved and percent of steers weigh over 1225 pounds is A = 19.3 %
Given data ,
The virginia cooperative extension reports that the mean weight of yearling angus steers is 1152 pounds
Now , weights of all such animals can be described by a normal model with a standard deviation of 84 pounds
First, we need to standardize the value 1225 pounds using the formula z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.
z = (1225 - 1152) / 84 = 0.869
Next, we can use a standard normal distribution table or a calculator to find the area under the curve to the right of z = 0.869. The corresponding probability represents the percentage of steers that weigh over 1225 pounds.
Using a standard normal distribution table, we find that the area to the right of z = 0.869 is approximately 0.193. This means that about 19.3% of steers weigh over 1225 pounds.
Hence , about 19.3% of yearling angus steers would be expected to weigh over 1225 pounds based on the given normal model
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Approximately 19.26% of yearling Angus steers weigh over 1225 pounds. This was calculated using the z-score derived from the normal distribution model with the given mean and standard deviation. The z-score translates to a percentile from which the percentage over 1225 pounds is derived.
The problem requires us to calculate the percentage of yearling Angus steers that weigh over 1225 pounds, given that the weights follow a normal distribution with a mean of 1152 pounds and a standard deviation of 84 pounds.
First, we need to find the z-score corresponding to a weight of 1225 pounds. The z-score formula is:
Z = (X - μ) / σ
where X is the value of interest, μ is the mean, and σ is the standard deviation.
Substitute the given values into the formula:
Z = (1225 - 1152) / 84
Z ≈ 0.869
Next, we use the z-score to find the corresponding percentile in the standard normal distribution table. A z-score of 0.869 corresponds approximately to the 80.74th percentile.
To find the percentage of steers that weigh more than 1225 pounds, subtract the percentile from 100%
100% - 80.74% ≈ 19.26%
Thus, about 19.26% of yearling Angus steers weigh over 1225 pounds.
