SOLUTION: Hello! My question is: The weights of ripe watermelons grown at Mr. Smith's farm are normally distributed with a standard deviation of 2.8 lbs. Find the mean weight of Mr.Smith's

Question 1030310: Hello!
My question is: The weights of ripe watermelons grown at Mr. Smith's farm are normally distributed with a standard deviation of 2.8 lbs. Find the mean weight of Mr.Smith's ripe watermelons if only 3% weigh less than 15lbs.
Thank you for your help!!
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
Hello!
My question is: The weights of ripe watermelons grown at Mr. Smith's farm are normally distributed with a standard deviation of 2.8 lbs. Find the mean weight of Mr.Smith's ripe watermelons if only 3% weigh less than 15lbs.

Solution:
This is a nice question that digs into the understanding of the Normal Distribution parameters.
If only 3% weigh less than 15 lbs, then we can find the standard deviation from 3% using the normal distribution table or function:
P(Z)=97%, Z=+1.8808.
Since standard deviation is given as 2.8 lbs, so
μ+1.8808*2.8=15 lbs, or
μ=15-1.8808*2.8=15-5.27=9.73 lb.
Ans. the mean weight is 9.73 lb. (approx.)
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