Please help :) Potatoes - Samples: Assume the weights of Farmer Carl\'s potatoes
ID: 3171570 • Letter: P
Question
Please help :) Potatoes - Samples: Assume the weights of Farmer Carl's potatoes are normally distributed with a mean of 9.0 ounces and a standard deviation of 1.2 ounces. He bags his potatoes in groups of 6. You buy a bag and the total weight is 48 ounces. Here we determine how lucky or unlucky you are.
1. If 6 potatoes are randomly selected, find the probability that the mean weight is less than the mean found in your bag
2. Which statement best describes your situation?
a This is an unusually small amount of potatoes. You are unlucky because the probability of getting a bag weighing less than yours is only about 2.1%.
b You got lucky with such a generous amount of potato your bag.
cYou got extremely unlucky because the probability of getting a bag weighing less than yours is about 0.01%.
dThis is not particularly unusual because the mean weight in your bag is only 1 ounce below the mean of all Carl's potatoes.
Explanation / Answer
Mean ( u ) =9
Standard Deviation ( sd )= 1.2/ Sqrt(n) = 0.4899
Number ( n ) = 6
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)
P(X < 8) = (8-9)/1.2/ Sqrt ( 6 )
= -1/0.4899= -2.0412
= P ( Z <-2.0412) From Standard NOrmal Table
= 0.021
a This is an unusually small amount of potatoes.
You are unlucky because the probability of getting a bag weighing less than yours is only about 2.1%.