A grocery store purchases watermelons. They are told the weight of the melons fo

Question

A grocery store purchases watermelons. They are told the weight of the melons follows a normal distribution with a mean of 16.0 lbs and a standard deviation of 2.0 lbs. a. What proportion of the melons are greater than 14 lbs? b. Watermelons under 10 lbs are considered unacceptable to the grocery store. What proportion of watermelons would be removed by the store? c. What proportion of watermelons are between 15 and 20 lbs? d. What is the median weight of the watermelons? e. One of the watermelons was 22 lbs. Was this an unusual sized melon? Why?

Explanation / Answer

1. It is 1 deviation below mean. Meaning P(X>14) = P(Z>-1) = .16+.5 = .66
2. P( X<10) = P(Z<-3) = 1-.997 / 2 = .0015
3. P( 15<X<20) = P(-.5<Z<2) = .475+.3085 = .7835
4. Median = mean = 16 ( 50ther percentile in normal dist)
5. P(X=22) = P(Z=22-16/2) = P(Z=3). The p value is .0015, which is very low and hence we can conclude that its unusual to get this sized melon. Because, the prob of getting this size melon is just .15%

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