Respuesta :
Answer:
The coach should start recruiting players with weight 269.55 pounds or more.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 225 pounds
Standard Deviation, σ = 43 pounds
We are given that the distribution of weights is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.15
[tex]P( X > x) = P( z > \displaystyle\frac{x - 225}{43})=0.15[/tex]
[tex]= 1 -P( z \leq \displaystyle\frac{x - 225}{43})=0.15[/tex]
[tex]=P( z \leq \displaystyle\frac{x - 225}{43})=0.85[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z < 1.036) = 0.85[/tex]
[tex]\displaystyle\frac{x - 225}{43} = 1.036\\\\x = 269.548 \approx 269.55[/tex]
Thus, the coach should start recruiting players with weight 269.55 pounds or more.
