Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 7.9 ounces and a standard deviation of 1.3 ounces.
(a) If 4 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces. Round your answer to 4 decimal places.
(b) If 7 potatoes are randomly selected, find the probability that the mean weight is more than 8.5 ounces. Round your answer to 4 decimal places.
Solution :
Given that ,
mean = = 7.9
standard deviation = = 1.3
(a)
n = 4
_{} = 7.9 and
_{} = / n = 1.3 / 4 = 1.3 / 2 = 0.65
P( < 9.3) = P(( - _{} ) / _{} < (9.3 - 7.9) / 0.65) = P(z < 2.1538)
Using standard normal table,
P( < 9.3) = 0.9844
Probability = 0.9844
(b)
n = 7
_{} = 7.9 and
_{} = / n = 1.3 / 7
P( > 8.5) = 1 - (P( < 8.5) = 1 - P(( - _{} ) / _{} < (8.5 - 7.9) / 1.3/7 = 1 - P(z < 1.2211)
Using standard normal table,
P( < 9.3) = 1 - 0.8890 = 0.1110
Probability = 0.1110
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