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sasho
14 days ago
9

A college football coach has decided to recruit only the heaviest 15% of high school football players. He knows that high school

players’ weights are normally distributed and that this year, the mean weight is 225 pounds with a standard deviation of 43 pounds. Calculate the weight at which the coach should start recruiting players.
Mathematics
1 answer:
Inessa [3.9K]14 days ago
3 0

Response:

The coach should begin seeking players who weigh at least 269.55 pounds.

Step-by-step explanation:

We have these details from the question:

Average, μ = 225 pounds

Standard Deviation, σ = 43 pounds

The weights follow a bell curve, indicating a normal distribution.

Formula:

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

We need to establish the value of x that corresponds to a probability of 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

Review from the standard normal z table gives us:

P(z < 1.036) = 0.85

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

Consequently, the coach should start recruiting players weighing at least 269.55 pounds.

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