A particular fruit's weights are normally distributed, with a mean of 758 grams and a standard deviation of 25 grams.
If you pick one fruit at random, what is the probability that it will weigh between 705 grams and 787 grams
To calculate the probability that a randomly selected fruit will weigh between 705 grams and 787 grams, we need to find the area under the normal distribution curve between these two weights.
First, let's standardize the weights using the z-score formula:
z = (x - μ) / σ
where x is the specific weight, μ is the mean weight, and σ is the standard deviation.
For a weight of 705 grams:
z1 = (705 - 758) / 25 = -2.12
For a weight of 787 grams:
z2 = (787 - 758) / 25 = 1.16
Now, we can find the probability associated with these z-scores using a standard normal distribution table or a calculator:
P(z1 < Z < z2) = P(-2.12 < Z < 1.16)
Looking up the probabilities associated with each z-score from the table, we find:
P(-2.12 < Z < 1.16) ≈ 0.8857
Therefore, the probability that a randomly selected fruit will weigh between 705 grams and 787 grams is approximately 0.8857, or 88.57%.