Answer:
The probability that maximum safe load will be exceeded is 3.9%
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 190 pounds
Standard Deviation, σ = 40 pounds
We are given that 50 skiers are randomly chosen from this normally distributed population, hence, by central limit theorem:
Mean, μ = 190 pounds
Standard Deviation,[tex]\sigma = \displaystyle\frac{40}{\sqrt{50}}\text{ pounds}[/tex]
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P(maximum safe load exceeded)
[tex]P( x > \frac{10000}{50}) = P( z > \displaystyle\frac{\frac{10000}{50} - 190}{\frac{40}{\sqrt{50}}}) = P(z > 1.767)[/tex]
[tex]= 1 - P(z \leq 1.767)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 10000) = 1 - 0.961 = 0.039= 3.9\%[/tex]
Hence, the probability that maximum safe load will be exceeded is 3.9%
