Mathematics: Critical observations thinking is the best deomstrated by which of the following action

Critical observations thinking is the best deomstrated

kim643

02.08.2020

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:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.15

$P( X x) = P( z \displaystyle\frac{x - 225}{43})=0.15$

$= 1 -P( z \leq \displaystyle\frac{x - 225}{43})=0.15$

$=P( z \leq \displaystyle\frac{x - 225}{43})=0.85$

Calculation the value from standard normal z table, we have,

P(z < 1.036) = 0.85

$\displaystyle\frac{x - 225}{43} = 1.036\\\\x = 269.548 \approx 269.55$

Thus, the coach should start recruiting players with weight 269.55 pounds or more.

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