Question

A fuel pump at a gasoline station doesn't always dispense the exact amount displayed on the meter. when the meter reads 1.000\text{ l}1.000 l1, point, 000, start text, space, l, end text, the amount of fuel a certain pump dispenses is normally distributed with a mean of 1\text{ l}1 l1, start text, space, l, end text and standard deviation of 0.05\text{ l}0.05 l0, point, 05, start text, space, l, end text. let xxx represent the amount dispensed in a random trial when the meter reads 1.000\text{ l}1.000 l1, point, 000, start text, space, l, end text. find p(x>1.05)p(x>1.05)p, left parenthesis, x, is greater than, 1, point, 05, right parenthesis.

Answer 1

Based on the calculations, the value of $P(x > 1.05)$ is approximately equal to 0.16.

Given the following data:

• Sample mean = 1.05

• Standard deviation = 0.05

• Mean = 1.000.

How to calculate the z-score.

In Mathematics, z-scores can either be negative or positive and it is generally calculated by using this formula:

$Z=\frac{x\;-\;u}{\delta}$

Where:

• x is the sample mean.

• u is the mean.

• $\delta$ is the standard deviation.

Substituting the given parameters into the formula, we have;

$Z=\frac{1.05\;-\;1.000}{0.05}\\\\Z=\frac{0.05}{0.05}$

Z = 1.0.

Therefore, we have;

$P(x > 1.05)=P(Z > 1)$

From the z-table, a z-score of 1.0 corresponds to or has a p-value of 0.1587. Therefore, the p-value for this test is 0.1587 > 1.05.

In conclusion, the value of $P(x > 1.05)$ is approximately equal to 0.16.

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