Final answer:
Using properties of a normal distribution, approximately 2 onions (rounded from 1.59) are expected to weigh more than 165 grams and the same number to weigh less than 135 grams. Therefore, the closest answer is option A.
Step-by-step explanation:
The question asks us to determine how many onions weigh more than 165 grams and how many weigh less than 135 grams out of 10 onions that follow a normal distribution with a mean weight of 150 grams and a standard deviation of 15 grams. We know from a normal distribution that approximately 68.2% of data falls within one standard deviation of the mean, 95.4% within two standard deviations, and 99.6% within three standard deviations.
Since 165 grams is one standard deviation (15 grams) above the mean, and 135 grams is one standard deviation below the mean, we can conclude that approximately 15.9% of the onions will weigh more than 165 grams and another 15.9% will weigh less than 135 grams. Applying these percentages to our sample of 10 onions, we would expect about 1.59 onions (or roughly 2 when rounded to the nearest whole number) to weigh more than 165 grams and another 1.59 onions to weigh less than 135 grams.
Thus, the closest answer from the options provided is A, suggesting that about 2 onions weigh more than 165 grams, and about 2 onions weigh less than 135 grams. The other options are not consistent with the properties of a normal distribution.