31. The weights of red delicious apples are approximately normally distributed w

Question

31. The weights of red delicious apples are approximately normally distributed with a mean of 9 ounces and a standard apples. At the time of deviation of 0.75 ounce. An online gift store sells gift boxes packaging. 5 red delicious apples are randomly selected and packaged in a box. containing 5 red delicious (a) Describe the distribution (i.e. give the mean and standard deviation) of the total weight of the 5 randomly selected red delicious apples (b) What is the probability that the total weight of the 5 randomly selected apples will be less than 42 ounces? (c) The combined weight of the packing material and box in which the apples will be shipped is always 10 ounces. Let W represent the weight of a complete packaged gift box, which consists of the packing material, box, and 5 randomly selected apples. What are the mean and the standard deviation of w?

Explanation / Answer

a)

distribution will be normal ; with mean =9*5=45

and std deviation =0.75*(5)1/2 =1.677

b)

probability =P(X<42) =P(Z<(42-45)/1.677) =P(Z<-1.7889)=0.0368

c)

mean of total weight W =E(W)=10+45 =55

and std deviation of W =1.677 (as weight of box being constant does not contribute in variability)

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