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 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

Answer 1

Answer:

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 2

Answer:

Step-by-step explanation:

Since the amount of fuel a certain pump dispenses is normally distributed, we would apply the normal distribution formula which is expressed as

z = (x - u)/s

Where

x = represent the amount dispensed in a random trial

u = mean amount

s = standard deviation

From the information given,

u = 1 L

s = 0.05L

We want to find P(X > 1.05) =

1 - P(X ≤ 1.05)

For x = 1.05,

z = (1.05 - 1)/0.05 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.84

P(X > 1.05) = 1 - 0.84 = 0.16