SOLUTION: fruits weight is normally distributed with mean of 480 and standard deviation of 37. if you pick 23 at random,then 3% of their mean weight will be greater than how many grams

Question 1161607: fruits weight is normally distributed with mean of 480 and standard deviation of 37. if you pick 23 at random,then 3% of their mean weight will be greater than how many grams

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z for 97th percentile is 1.881
z for this type of sampling distribution is (x bar-mean)/sigma/sqrt(n)
so
1.881=(x bar-480)*sqrt(23)/37
69.6/sqrt(23)=xbar-480=14.51
the mean weight will be greater than 494.5 grams in 3% of all possible samples of 23.
That's how I interpreted the problem.
If the author means 3% of the mean weight, or 14.835 grams is the answer. I've never seen that type of question before. I am assuming one wants the upper 3% of the distribution of mean weights.

RELATED QUESTIONS
A particular fruit's weights are normally distributed, with a mean of 491 grams and a... (answered by robertb)

A particular fruit's weights are normally distributed, with a mean of 481 grams and a... (answered by Theo)

A particular fruit's weights are normally distributed, with a mean of 453 grams and a... (answered by VFBundy)

A particular fruit's weights are normally distributed, with a mean of 375 grams and a... (answered by Theo,math_tutor2020)

The population of weights of a particular fruit is normally distributed, with a mean of... (answered by Theo)

A particular fruit's weights are normally distributed, with a mean of 657 grams and a... (answered by Boreal)

A particular fruit's weights are normally distributed, with a mean of 515 grams and a... (answered by Boreal)

A particular fruit's weights are normally distributed, with a mean of 410 grams and a... (answered by Boreal)

The SAT scores for MATH are normally distributed with a mean of 480 and a standard... (answered by jpg7n16)