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Diano4ka-milaya [45]
2 years ago
6

The weight of people in a small town in Missouri is known to be normally distributed with a mean of 162 pounds and a standard de

viation of 28 pounds. On a raft that takes people across the river, a sign states, “Maximum capacity 3,401 pounds or 19 persons.” What is the probability that a random sample of 19 persons will exceed the weight limit of 3,401 pounds?
Mathematics
1 answer:
never [62]2 years ago
8 0

Using the normal distribution relation, the probability that sample will exceed the weight limit is 0.004

<u>Using the relation</u> ::

  • Zscore =(X - μ) ÷ σ

The mean, μ = np = (162 × 19) = 3078

The standard deviation, σ = 28 × √19 = 122.049

<u>The Zscore</u> :

Zscore = (3401 - 3078) ÷ (122.049)

Zscore = 2.65

Hence,

P(Z > 2.65) = 1 - P(Z < 2.65)

Using a normal distribution table :

P(Z > 2.65) = 1 - 0.9959

P(Z > 2.65) = 0.004

Learn more : brainly.com/question/25204474

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