Respuesta :
Answer:
The empirical rule (or the 68-95-99.7 rule) states that for a normally distributed data set, approximately:
68% of the data falls within 1 standard deviation of the mean.
95% of the data falls within 2 standard deviations of the mean.
99.7% of the data falls within 3 standard deviations of the mean.
In this case, the mean diameter is 7.44cm and the standard deviation is 0.45cm. We want to find the percentage of apples with diameters between 6.54cm and 8.34cm, which is 2 standard deviations from the mean:
One standard deviation below the mean: 7.44 cm - 0.45 cm = 6.99 cm
One standard deviation above the mean: 7.44 cm + 0.45 cm = 7.89 cm
Two standard deviations below the mean: 6.99 cm - 0.45 cm = 6.54 cm
Two standard deviations above the mean: 7.89 cm + 0.45 cm = 8.34 cm
The empirical rule tells us that approximately 95% of the apples will have diameters within 2 standard deviations of the mean, which is between 6.54cm and 8.34cm.
Therefore, approximately 95% of the apples have diameters that fall within the specified range.
