Mathematics, 11.02.2021 17:40 adejumoayobami1

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. The probability of a player weighing more than 250 pounds is Group of answer choices 0.9505 0.9772 0.0228 0.4505 0.0495

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Answer from: joelpimentel

0.0228

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.

This means that $\mu = 200, \sigma = 25$

The probability of a player weighing more than 250 pounds is

This is 1 subtracted by the pvalue of Z when X = 250. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{250 - 200}{25}$

Z = 2

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

The probability of a player weighing more than 250 pounds is 0.0228

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

step-by-step explanation:

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The weight of football players is normally distributed with a mean of 200 pounds and a standard devi...