Chapter 5: Q. 5.24 (page 213)

The lifetimes of interactive computer chips produced
by a certain semiconductor manufacturer are normally distributed with parameters $μ = 1.4 \times 10^{6}$ hours and $σ = 3 \times 10^{5}$ hours. What is the approximate probability that abatch of $100$ chips will contain at least $20$ whose lifetimes are less than $1.8 \times 10^{6}$ ?

Short Answer

Expert verified

The required probability is $1$ .

Step by step solution

Step 1. Given information.

Here, it is given that the lifetimes of interactive computer chips are normally distributed with parameters

$μ = 1.4 \times 10^{6} hours σ = 3 \times 10^{5} hours$

Step 2. Find the life time of an interactive computer chip.

Let $X$ denote the life time of an interactive computer chip.

$P (X \leq 1.8 \times 10^{6}) = P (Z \leq \frac{1.8 \times 10^{6} - 1.4 \times 10^{6}}{3 \times 10^{5}}) = P (Z \leq 1.333) = 0.9082$

Step 3. Find the probability that a batch of 100chips will contain at least 20 such chips whose life times are less than 1.8×106.

$p = 0.9082 μ = n p = 100 \times 0.9082 = 90.82 σ = \sqrt{n p q} = \sqrt{90.82 (1 - 0.9082)} = 2.89$

$P (Y \geq 19.5) = P (z \geq \frac{19.5 - 90.82}{2.89}) = P (z \geq - 24.678) ≅ 1$

Therefore, the approximate probability that a batch of $100$ chips will contain at least 20 such chips whose life times are less than $1.8 \times 10^{6}$ is $1$ .

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!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the life time of an interactive computer chip.

Step 3. Find the probability that a batch of 100chips will contain at least 20 such chips whose life times are less than 1.8×106.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Pure Maths

Decision Maths

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

The lifetimes of interactive computer chips producedby a certain semiconductor manufacturer are normally distributed with parametersμ=1.4×106hours and σ=3×105hours. What is the approximate probability that abatch of 100chips will contain at least 20whose lifetimes are less than 1.8×106?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the life time of an interactive computer chip.

Step 3. Find the probability that a batch of 100chips will contain at least 20 such chips whose life times are less than 1.8×106.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Pure Maths

Decision Maths

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.