The weight of people in a small town in Missouri is known to be normally distributed with a mean of 180 pounds and a standard deviation of 28 pounds. On a raft that takes people across the river, a sign states, “Maximum capacity 3,200 pounds or 16 persons.” What is the probability that a random sample of 16 persons will exceed the weight limit of 3,200 pounds
The weight of people in a small town in Missouri is known to be
Provided data is,
The weight of people in a small town in Missouri is known to be normally distributed with a mean of 180 pounds and a standard deviation of 28 pounds.
Let X is variable for weight of people in town.
X~ N(µ=180, σ2=282)
Randomly 16 persons are selected.
According to property of normal distribution
if X~ N(µ, σ2) then ΣX~ N(nµ, nσ2)
Thus, here ΣX~ N(16(180), 16(282)) i.e. ΣX~ N(µ=2880, σ2=1122)
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