A grocery store purchases melons from two distributors, J and K. Distributor J p

Question

A grocery store purchases melons from two distributors, J and K. Distributor J provides melons from organic farms. The distribution of the diameters of the melons from Distributor J is approximately normal with mean 133 millimeters (mm) and standard deviation 5 mm. (a) For a melon selected at random from Distributor J, what is the probability that the melon will have a diameter greater than 137 mm? Distributor K provides melons from nonorganic farms. The probability is 0.8413 that a melon selected at random from Distributor K will have a diameter greater than 137 mm. For all the melons at the grocery store, 70 percent of the melons are provided by Distributor J and 30 percent are provided by Distributor K. (b) For a melon selected at random from the grocery store, what is the probability that the melon will have a diameter greater than 137 mm? (c) Given that a melon selected at random from the grocery store has a diameter greater than 137 mm, what is the probability that the melon will be from Distributor J?

Explanation / Answer

a)P(X>137)=1-P(X<137)=1-P(Z<(137-133)/5)=1-P(Z<0.8)=1-0.7881=0.2119

b) probabilty X>137 =from distributor J and have X>137+from distributor K and haveX>137

=0.7*0.2119+0.3*0.8413=0.4007

c)probabilty from Distributor J, given dia is greater then 137 =0.7*0.2119/0.4007=0.3702

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