A fuel 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 = the amount dispensed in a random trial when the meter reads
1.000 L
Find P(X < 1).

P(X < 1) = 0.5

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 1 L and standard deviation of 0.05 L.

This means that

Find P(X < 1).

This is the p-value of Z when X = 1. So

has a p-value of 0.5. Thus

P(X < 1) = 0.5

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