Mathematics, 10.01.2020 06:31 ur4286

Afuel pump at a gasoline station doesn't always dispense the exact amount displayed on the meter. when the meter reads 1.000 l, the amount of fuel a certain pump dispenses is normally distributed with a mean of 1 l and standard deviation of 0.05 l. let x represent the amount dispensed in a random trial when the meter reads 1.000 l find p(x > 1.05). you may round your answer to two decimal places

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Answer from: kevin72937

The value of P(x > 1.05) is 0.16

The given parameters are:

$\mathbf{\sigma = 0.05}$ --- the standard deviation

$\mathbf{\mu = 1.000}$ --- the mean

$\mathbf{x = 1.05}$ --- the sample reading

Start by calculating the z-score for x = 1.05 using:

$\mathbf{z = \frac{x - \mu}{\sigma}}$

So, we have:

$\mathbf{z = \frac{1.05 - 1}{0.05}}$

$\mathbf{z = 1}$

So, we have:

$\mathbf{P(x 1.05) = P(z 1)}$

From z table of probabilities, we have:

$\mathbf{P(z 1) = 0.1587}$

This means that:

$\mathbf{P(x 1.05) = 0.1587}$

Approximate

$\mathbf{P(x 1.05) = 0.16}$

Hence, the value of P(x > 1.05) is 0.16

Read more about probabilities at:

link

Answer from: azinanees

P(X > 1.05) = 1 - 0.8413 = 0.1587 = 15.87%.

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:

$\mu = 1, \sigma = 0.05$

Find P(X > 1.05).

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

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

$Z = \frac{1.05 - 1}{0.05}$

Z = 1

Z = 1 has a pvalue of 0.8413

So P(X > 1.05) = 1 - 0.8413 = 0.1587 = 15.87%.

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

Answer from: Quest

a is 8.b is 10.c is 10.5. d is -.5

step-by-step explanation:

just minus the smallest number from the biggest.

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