The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.4 years and a standard deviation of 0.5 years. He then randomly selects records on 37 laptops sold in the past. Round the answers of following questions to 4 decimal places. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the probability that one randomly selected laptop is replaced less than 4.5 years?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
icon
Related questions
Question

The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.4 years and a standard deviation of 0.5 years. He then randomly selects records on 37 laptops sold in the past. Round the answers of following questions to 4 decimal places.

  1. What is the distribution of XX? XX ~ N(,)
  2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
  3. What is the probability that one randomly selected laptop is replaced less than 4.5 years? 
Expert Solution
Step 1

 

(1)

 

Determine the distribution of X.

 

The distribution of X is obtained below as follows:

Statistics homework question answer, step 1, image 1

Step 2

(2)

Statistics homework question answer, step 2, image 1

Thus, the value of sample mean of the sampling distribution is 4.4.

 

The value of the sampling distribution of the standard deviation is,

 

Statistics homework question answer, step 2, image 2

steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill