Mathematics, 28.07.2019 13:00 slayalways

The miles-per-gallon obtained by the 1995 model q cars is normally distributed with a mean of 22 miles-per-gallon and a standard deviation of 5 miles-per-gallon. what is the probability that a car will get less than 21 miles-per-gallon? (4 decimal format = 0.0000)

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That probability is about 0.4207.
The miles-per-gallon obtained by the 1995 model q cars is normally distributed with a mean of 22 mil

Answer from: Trup1822

The probability that a car will get less than 21 miles-per-gallon is 0.4207.

Step-by-step explanation:

Problems of normally distributed samples can be solved using 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.

In this problem, we have that:

$\mu = 22, \sigma = 5$

What is the probability that a car will get less than 21 miles-per-gallon?

This probability is the pvalue of Z when X = 21 . So

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

$Z = \frac{21 - 22}{5}$

Z = -0.2

Z = -0.2 has a pvalue of 0.4207.

So the probability that a car will get less than 21 miles-per-gallon is 0.4207.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

step-by-step explanation:

14 x 3 = 42

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