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ANEK [815]
3 years 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:
Alla [95]3 years ago
3 0

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:

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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To find the value of q, we need to find d(-8). Put another way, we need to find the value of d(x) when x = -8

d(x) = -\sqrt{\frac{1}{2}x+4}

d(-8) = -\sqrt{\frac{1}{2}(-8)+4}

d(-8) = -\sqrt{-4+4}

d(-8) = -\sqrt{0}

d(-8) = 0

So this means q = 0. Note that -0 is just 0.

===========================================

The value of r will be a similar, but now we use f(x) this time.

Plug in x = 0

f(x) = \sqrt{\frac{1}{2}x+4}

f(0) = \sqrt{\frac{1}{2}*0+4}

f(0) = \sqrt{0+4}

f(0) = \sqrt{4}

f(0) = 2

Therefore, r = 2.

===========================================

For s, we plug x = 10 into f(x)

f(x) = \sqrt{\frac{1}{2}x+4}

f(10) = \sqrt{\frac{1}{2}*10+4}

f(10) = \sqrt{5+4}

f(10) = \sqrt{9}

f(10) = 3

So s = 3.

===========================================

Finally, plug x = 10 into d(x) to find the value of t

d(x) = -\sqrt{\frac{1}{2}x+4}

d(10) = -\sqrt{\frac{1}{2}(10)+4}

d(10) = -\sqrt{5+4}

d(10) = -\sqrt{9}

d(10) = -3

A shortcut you could have taken is to note how d(x) = -f(x), so this means

d(10) = -f(10) = -9 since f(10) = 9 was found in the previous section above.

Whichever method you use, you should find that t = -3.

===========================================

<h3>In summary:</h3><h3>q = 0</h3><h3>r = 2</h3><h3>s = 3</h3><h3>t = -3</h3>
8 0
3 years ago
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