Question

A particular fruit's weights are normally distributed with a mean of 386 grams and a standard deviation of 11 grams. If you pick one fruit at random, what is the probability that it will weigh between 372 grams and 388 grams?

Answer 1

The probability that a randomly selected fruit will weigh between 372 grams and 388 grams, given a normal distribution with a mean of 386 grams and standard deviation of 11 grams, is approximately 46.94%.

Step-by-step explanation:

To calculate the probability that a randomly selected fruit will weigh between 372 grams and 388 grams, given that the weights are normally distributed with a mean of 386 grams and a standard deviation of 11 grams, we can use the z-score formula:

Z = (X - μ) / σ
Where X is the value for which we want to find the probability, μ is the mean, and σ is the standard deviation.

Calculating the z-scores for 372 grams and 388 grams:

1. For 372 grams: Z = (372 - 386) / 11 = -14 / 11 ≈ -1.27
2. For 388 grams: Z = (388 - 386) / 11 = 2 / 11 ≈ 0.18

Now, we can look up these Z-values in a standard normal distribution table or use a calculator that provides the probability for these Z-values. The probability for a z-score of -1.27 is approximately 0.1020, and for a z-score of 0.18 is approximately 0.5714. To find the probability between the two Z-values, we subtract the smaller probability from the larger one:

Probability = P(0.18) - P(-1.27) = 0.5714 - 0.1020 = 0.4694 or 46.94%

The probability that a randomly selected fruit will weigh between 372 grams and 388 grams is approximately 46.94%.