Final answer:
To find the range in which at least 80% of the data will lie, we can use the z-score formula and the given mean and standard deviation. Therefore, the range in which at least 80% of the data will lie is approximately (0.22 - 0.44) lb.
Step-by-step explanation:
To find the range in which at least 80% of the data will lie, we need to calculate the z-score associated with that percentage. The z-score represents the number of standard deviations away from the mean. Since we want to find the range, we need to calculate both the upper and lower values.
To find the lower value, we subtract the z-score multiplied by the standard deviation from the mean. To find the upper value, we add the z-score multiplied by the standard deviation to the mean. Plugging in the values given, we get:
Lower value = 0.33 - (z-score * 0.13)
Upper value = 0.33 + (z-score * 0.13)
Using a z-score table or calculator, we find that the z-score for 80% is approximately 0.84. Plugging in this value, we get:
Lower value = 0.33 - (0.84 * 0.13) = 0.2192
Upper value = 0.33 + (0.84 * 0.13) = 0.4408
Therefore, the range in which at least 80% of the data will lie is approximately (0.22 - 0.44) lb.