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

The value of P(x > 1.05) is 0.16

The given parameters are:

--- the standard deviation

--- the mean

--- the sample reading

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

So, we have:

So, we have:

From z table of probabilities, we have:

This means that:

Approximate

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

Read more about probabilities at:

link

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 and standard deviation , the zscore of a measure X is given by:

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:

Find P(X > 1.05).

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

has a pvalue of 0.8413

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

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