A fuel injection system is designed to last 18 years, with a standard deviation of 1.4 years. What is the probability that a fuel injection system will last less than 15 years? 25% 33% 2% 20%

Using the normal distribution, it is found that there is a 2% probability that a fuel injection system will last less than 15 years.

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

In this problem:

The probability that a fuel injection system will last less than 15 years is 1 subtracted by the p-value of Z when X = 15, hence:

has a p-value of 0.02.

0.02 = 2% probability that a fuel injection system will last less than 15 years.

To learn more about the normal distribution, you can take a look at link

2%

Step-by-step explanation:

We are given;

Standard Design mean; μ = 18

Sample design mean; x¯ = 15

Standard Standaed deviation; σ = 1.4

Let's find the test statistic from the formula;

z = (x¯ - μ)/σ

Thus;

z = (15 - 18)/1.4

z = -2.14

From the z-table attached, the p-value at z = -2.14 is 0.01618

Thus,

P(X < 15) = 0.01618

Converting to percentage, we have

P(X < 15) = 1.618%

This is approximately 2%

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step-by-step explanation:

step-by-step explanation: