Question

A particular fruit's weights are normally distributed, with a mean of 758 grams and a standard deviation of 14 grams. If you pick one frult at random, what is the probability that it will weigh between 710 grams and 721 grams .

Answer 1

To find the probability that a randomly picked fruit weighs between 710 grams and 721 grams, we need to standardize the weights using z-scores and calculate the probability associated with these z-scores.

Step-by-step explanation:

To find the probability that a randomly picked fruit weighs between 710 grams and 721 grams, we need to find the area under the normal distribution curve between these two weights. First, we need to standardize the weights by calculating the z-scores for each weight. The z-score formula is (x - mean) / standard deviation. For 710 grams, the z-score is (710 - 758) / 14 = -3.43, and for 721 grams, the z-score is (721 - 758) / 14 = -2.64. Using a standard normal distribution table or a calculator, we can find the probability associated with these z-scores. The probability will be the difference between the two values: P(-3.43 < z < -2.64). By referring to the standard normal distribution table, we find that the probability is approximately 0.0207.