Answer :
1. The proportion of individuals that weighed 143 lbs or less is approximately 2.08.
2. The proportion of individuals who weighed between 147 lbs and 180 lbs is approximately -1.75 and 1.
3. The proportion of individuals who weighed 200 lbs or more is approximately 2.67.
1: To calculate these proportions, we need to standardize the weights using the z-score formula:
z = (x - μ) / σ
Where:
x is the weight
μ is the mean weight
σ is the standard deviation
1. For 143 lbs or less:
z = (143 - 168) / 12 = -2.08
The proportion is the area under the standard normal curve to the left of 2.08 (taking absolute value).
2. For 147 lbs to 180 lbs:
z = (147 - 168) / 12 = -1.75
z = (180 - 168) / 12 = 1
The proportion is the area under the standard normal curve between -1.75 and 1.
3. For 200 lbs or more:
z = (200 - 168) / 12 = 2.67
The proportion is the area under the standard normal curve to the right of 2.67.
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Question
In a study to examine variations in body weight over a one-year period, the mean weight was 168 Ibs with a standard deviation of 12 Ibs. Assuming that weight is normally distributed,
Find:
the proportion of individuals that weighed 143 lbs or less
the proportion who weighed between 147 lbs and 180 lbs
the proportion who weighed 200 lbs or more
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