QuestionFind the standard deviation of human pregnancy lengths given a mean of 267 days and a range of 245 to 289 days. What percent last at least 285 days?
Studdy Solution
STEP 1
Assumptions1. The mean length of a human pregnancy is267 days.
.95% of all human pregnancies last between245 and289 days.
3. We are assuming a normal distribution of lengths of human pregnancies.
4. We are looking for the standard deviation of this distribution.
5. We are also looking for the percentage of pregnancies that last at least285 days.
STEP 2
First, let's find the standard deviation. For a normal distribution,95% of the data falls within2 standard deviations of the mean. So, the range from245 to289 days represents4 standard deviations.
STEP 3
Now, plug in the given values to calculate the standard deviation.
STEP 4
To find the standard deviation, divide the result by4.
STEP 5
Calculate the standard deviation.
The standard deviation of the distribution of lengths of human pregnancies is11 days.
STEP 6
Now, let's find the percentage of pregnancies that last at least285 days. In a normal distribution, the area under the curve to the right of a value is the percentage of data that is greater than that value.Since the mean is267 days and the standard deviation is11 days, the value of285 days is more than1 standard deviation but less than2 standard deviations away from the mean.In a normal distribution, about68% of the data falls within1 standard deviation of the mean, about95% falls within2 standard deviations, and about99.% falls within3 standard deviations.So, the percentage of pregnancies that last at least285 days is less than5% but more than0.3%. Given the options, we can conclude that the percentage is5%.
The percent of human pregnancies that are expected to last at least285 days is5%.
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