The weight of people in a small town in Missouri is known to be normally distrib

Question

The weight of people in a small town in Missouri is known to be normally distributed with a mean of 177 pounds and a standard deviation of 28 pounds. On a raft that takes people across the river, a sign states, "Maximum capacity 3, 528 pounds or 18 persons." What is the probability that a random sample of 18 persons will exceed the weight limit of 3, 528 pounds? Use Table 1. (Round your intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) Probability _____

Explanation / Answer

mean = 177 , s = 28 , n =18

x = 3528/18 = 196

BY NORMAL DISTRIBUTION FORMULA,

z = ( x -mean) / ( s / sqrt(n))

= ( 196 - 177) / ( 28/sqrt(18))

= 2.88

now, we need to find p( z> 2.88)

P(x >196) = P(z > 2.88) = 0.002

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