A sample of the monthly amounts spent for food by families of four receiving food stamps approximates asymmetrical distribution. The sample mean is $150 and the standard deviation is $20. About 95 percent of the monthly food expenditures are between what two amounts?
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A. B. C. D. E.B
About 95% of the observations lie between plus and minus two standard deviations from the mean.
To determine the range of monthly food expenditures within which approximately 95 percent of the families fall, we can use the concept of standard deviations and the properties of a normal distribution.
In a normal distribution, about 68 percent of the data falls within one standard deviation from the mean, about 95 percent falls within two standard deviations, and about 99.7 percent falls within three standard deviations.
Given that the sample mean is $150 and the standard deviation is $20, we can apply these properties to estimate the range.
Within two standard deviations of the mean ($150 ± 2 * $20), we would expect approximately 95 percent of the data to fall.
Lower bound: $150 - (2 * $20) = $150 - $40 = $110 Upper bound: $150 + (2 * $20) = $150 + $40 = $190
Therefore, approximately 95 percent of the monthly food expenditures are expected to be between $110 and $190.
Among the given answer choices, the correct option is B. $110 and $190.