Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 23: Problem 3

Studies of a particular type of car tyre show that the mileage for which it can be used legally follows a normal distribution with mean 38000 miles and standard deviation 2500 miles. The manufacturers claim that ' 9 out of 10 of our tyres last more than 35000 miles'. Is the claim justified?

Short Answer

Expert verified
Answer: No, the manufacturer's claim is not justified as the probability of tyres lasting more than 35000 miles is 0.8849 (88.49%), which is less than 90%.

Step by step solution

01

Identify the given values

We are given the following information: Mean (μ) = 38000 miles Standard deviation (σ) = 2500 miles Mileage limit (X) = 35000 miles
02

Calculate the Z-score

We will use the Z-score formula to convert the mileage limit to a standard Z-score: Z = (X - μ) / σ Substitute the given values: Z = (35000 - 38000) / 2500 Z = -3000 / 2500 Z = -1.2
03

Find the probability from the Z-score

Now we need to find the probability associated with this Z-score using the standard normal distribution table: P(Z > -1.2) = 1 - P(Z <= -1.2) Looking up the value of P(Z <= -1.2) in the standard normal distribution table, we get 0.1151. Now, subtract this from 1 to get P(Z > -1.2): P(Z > -1.2) = 1 - 0.1151 = 0.8849
04

Compare the probability to the manufacturer's claim

To justify the manufacturer's claim, the probability of tyres lasting more than 35000 miles should be greater than or equal to 0.9 (90%): 0.8849 >= 0.9 Since 0.8849 is not greater than or equal to 0.9, the manufacturer's claim of "9 out of 10 of our tyres last more than 35000 miles" is NOT justified.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The probability that a component is acceptable is \(0.91\). Ten components are picked at random. Calculate the probability that (a) eight are acceptable (b) more than eight are acceptable (c) three are not acceptable.

The probability that a machine has a lifespan of more than 7 years is \(0.85\). Twelve machines are chosen at random. Calculate the probability that (a) 10 have a lifespan of more than 7 years (b) 11 have a lifespan of more than 7 years (c) 10 or more have a lifespan of more than 7 years.

On any day, the probability that a person is absent due to illness is \(0.001\). In a workforce of 600 people, calculate the probability that on any day the number of people absent is (a) none, (b) one, (c) more than one, (d) less than three.

The probability that a motor will malfunction within 5 years of manufacture is \(0.03\). Out of eight motors calculate the probability that within 5 years of manufacture (a) all eight will malfunction (b) six will malfunction (c) none will malfunction.

Components are manufactured by three machines, \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\). Machine A makes \(30 \%\) of the components, machine B makes \(25 \%\) of the components and machine \(\mathrm{C}\) makes the rest. Of those components made by machine A, \(6 \%\) are substandard; when made by machine B, \(3 \%\) are substandard; and when made by machine C, \(5 \%\) are substandard. A component is picked at random. Calculate the probability that it is (a) substandard (b) made by machine B given it is substandard (c) made by either machine \(\mathrm{A}\) or machine \(\mathrm{B}\) (d) substandard and made by machine B (e) substandard, given it is made by machine \(\mathrm{A}\) (f) made by machine A or is substandard.
See all solutions

Recommended explanations on Physics Textbooks

Astrophysics

Read Explanation

Measurements

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Famous Physicists

Read Explanation

Waves Physics

Read Explanation

Wave Optics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free