Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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%

Sagot :

Answer:

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%

View image AFOKE88

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

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • It 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, which is the percentile of X.

In this problem:

  • The mean is of 18 years, hence [tex]\mu = 18[/tex].
  • The standard deviation is of 1.4 years, hence [tex]\sigma = 1.4[/tex].

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:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{15 - 18}{1.4}[/tex]

[tex]Z = -2.14[/tex]

[tex]Z = -2.14[/tex] 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 https://brainly.com/question/24663213

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.