Type the correct answer in each box. Use numerals instead of words.
The weights of 1,000 onions from a certain farm follow a normal distribution with a mean of 150 grams and a standard deviation of 15 grams.
From the data, we can conclude that about ___ onions weigh more than 165 grams and about ___ onions weigh less than 135 grams.
From the given information, we can calculate the z-scores for both weights using the formula:
z = (x - μ) / σ
For weights more than 165 grams:
z1 = (165 - 150) / 15
And for weights less than 135 grams:
z2 = (135 - 150) / 15
Using a standard normal distribution table or calculator, we can find the probabilities associated with these z-scores.
For z1 = (165 - 150) / 15 = 1,
the probability of an onion weighing more than 165 grams is approximately 0.1587.
For z2 = (135 - 150) / 15 = -1,
the probability of an onion weighing less than 135 grams is approximately 0.1587.
Therefore, about 158.7 onions weigh more than 165 grams and about 158.7 onions weigh less than 135 grams.