If you pick 11 fruits at random, then 7% of the time, their mean weight will be greater than how many grams?

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 11 fruits at random, then 7% of the time, their mean weight will be greater than how many grams?

Give your answer to the nearest gram.

Answer 1

Hi Kaitlyn,

Amazing question!

We are dealing with weights of a particular fruit that follow a normal distribution. The mean weight is 758 grams and the standard deviation is 14 grams. We want to find the weight that is exceeded 7% of the time when we pick 11 fruits randomly.

Step 1: Calculate the standard deviation of the sample mean. The formula is: Standard deviation of sample mean = Standard deviation / sqrt(Sample size) Here, Standard deviation = 14 grams and Sample size = 11. The calculated standard deviation of the sample mean is approximately 4.22 grams.

Step 2: Find the Z-score for the 93rd percentile, because we are interested in the top 7% (100% - 7% = 93%). The Z-score is approximately 1.476.

Step 3: Use the Z-score to find the weight that is exceeded 7% of the time. The formula is: Weight = Mean + (Z-score * Standard deviation of sample mean) Here, Mean = 758 grams and Standard deviation of sample mean = 4.22 grams.

The weight that will be exceeded 7% of the time when picking 11 fruits at random is approximately 764 grams, rounded to the nearest gram.

Thank you,

Benjamin M.

p.s. If this answer was helpful to you, I would greatly appreciate your feedback as I am new to this platform and it is incredibly helpful! :)