1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
madreJ [45]
3 years ago
6

The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than av

erage quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.3 years and a standard deviation of 0.6 years. He then randomly selects records on 50 laptops sold in the past and finds that the mean replacement time is 3.1 years.
Assuming that the laptop replacement times have a mean of 3.3 years and a standard deviation of 0.6 years, find the probability that 50 randomly selected laptops will have a mean replacement time of 3.1 years or less.
P(M < 3.1 years) =
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Based on the result above, does it appear that the computer store has been given laptops of lower than average quality?

No. The probability of obtaining this data is high enough to have been a chance occurrence.
Yes. The probability of this data is unlikely to have occurred by chance alone
Mathematics
1 answer:
34kurt3 years ago
8 0

Answer:

Probability that the 50 randomly selected laptops will have a mean replacement time of 3.1 years or less is 0.0092.

Yes. The probability of this data is unlikely to have occurred by chance alone.

Step-by-step explanation:

We are given that the replacement times for the model laptop of concern are normally distributed with a mean of 3.3 years and a standard deviation of 0.6 years.

He then randomly selects records on 50 laptops sold in the past and finds that the mean replacement time is 3.1 years.

<em>Let M = sample mean replacement time</em>

The z-score probability distribution for sample mean is given by;

            Z = \frac{ M-\mu}{\frac{\sigma}{\sqrt{n} } }} }  ~ N(0,1)

where, \mu = population mean replacement time = 3.3 years

            \sigma = standard deviation = 0.6 years

            n = sample of laptops = 50

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the 50 randomly selected laptops will have a mean replacement time of 3.1 years or less is given by = P(M \leq 3.1 years)

 P(M \leq 3.1 years) = P( \frac{ M-\mu}{\frac{\sigma}{\sqrt{n} } }} } \leq \frac{ 3.1-3.3}{\frac{0.6}{\sqrt{50} } }} } ) = P(Z \leq -2.357) = 1 - P(Z \leq 2.357)

                                                           = 1 - 0.99078 = <u>0.0092</u>  or  0.92%          

<em>So, in the z table the P(Z </em>\leq<em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2.357 in the z table which will lie between x = 2.35 and x = 2.36 which has an area of 0.99078.</em>

Hence, the required probability is 0.0092 or 0.92%.

Now, based on the result above; <u>Yes, the computer store has been given laptops of lower than average quality</u> because the probability of this data is unlikely to have occurred by chance alone as the probability of happening the given event is very low as 0.92%.

You might be interested in
Can someone help me please ? Thanks!
notka56 [123]
Use pythagorean theorem for all of them
a. 3, 4, 5
3^2+4^2?5^2
9+16?25
25=25
right 

b. 5, 6, 7
5^2+6^2=7^2
25+36=49
61>49
acute

c. 64+81=144
145>144
acute

hope this helps!
6 0
3 years ago
Read 2 more answers
What is the sum of 153 and 121
Gre4nikov [31]
     153
   <u>+121</u>
     274

Hope this helps!
7 0
3 years ago
The physics department of a college has 8 male professors, 11 female professors, 16 male teaching assistants, and 6 female teach
Lera25 [3.4K]
To determine the probability that one or the other circumstances will occur, you will count the number of possible outcomes and divide it by all the possible outcomes.

#of female teaching assistants + # of male teaching assistants + # of female professors

6 + 16 + 11 = 33

Total = 41

33/41 = 80

There is a approximate 80% probability that one or the other will occur.
6 0
3 years ago
Read 2 more answers
How can you solve real-world and mathematical problems with numerical and algebraic equations and inequalities?
Oliga [24]
You can solve real-world and mathematical problems with numerical and algebraic equations and inequalities. Algebra can be applied to the temperature in different places that both change, height of a growing child over time, the speed of a car that changes over time (mph), and the age of people that increases over year. Algebra is used in parts of our everyday life, we just don’t realize it.
7 0
3 years ago
Answer to be named brainliset get 25 pts and get a thank you
lisabon 2012 [21]

Answer:

The scale factor is .625 is false The scale factor 1.6 is true

Step-by-step explanation:

Since the triangle gets bigger the multiplication factor needs to be more than one to make the end result bigger

4 0
3 years ago
Other questions:
  • Help please I don’t know how to do this!!
    8·2 answers
  • Clark and Lana take a 30-year home mortgage of $128,000 at 7.8%, compounded monthly. They make their regular monthly payments fo
    9·1 answer
  • Perched upon Pinnacle Point, Peter picks up a peculiar piece of parchment (pictured below).
    11·2 answers
  • Use the remainder Theorem to find the remainder for (x2- 2)/(x - 1) and state whether or not the binomial is a factor of
    15·1 answer
  • helppppPPPppppPPppppppPppppPPpppPPPPpppPPPpppPppppPPPpPPPpppp please help do not look this up thank you
    9·1 answer
  • 483 divided by 2 because idk what the remaining numer will be
    7·1 answer
  • A box contains
    10·2 answers
  • I need help <br><br><br><br> Negehejrvrkrvrnrbr
    11·1 answer
  • PLEASE HELP ME WITH THIS QUESTION I REALLY NEED HELP
    7·1 answer
  • What's the sum of 14 12 8 6
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!