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
aleksley [76]
3 years ago
10

It is known that the life of a particular auto transmission follows a normal distribution with mean 72,000 miles and standard de

viation of 12,000 miles. a. A manufacturer warranties the transmission up to 40,000 miles. What percent of the transmissions will fail before the end of the warranty period? Would it be unusual for a transmission to expire before the warranty period? Explain. b. What percent of the transmissions will last longer than 65,000 miles? c. What percent of the transmissions last longer than 100,000 miles? Is this unusual? d. A transmission in the top 10% has been running for how many miles?
Mathematics
1 answer:
scoray [572]3 years ago
5 0

Answer:

a) P(X

P(z

b) P(X>65000)=P(\frac{X-\mu}{\sigma}>\frac{65000-\mu}{\sigma})=P(Z>\frac{65000-72000}{12000})=P(z>-0.583)

P(z>-0.583)=1-P(Z

c) P(X>100000)=P(\frac{X-\mu}{\sigma}>\frac{100000-\mu}{\sigma})=P(Z>\frac{100000-72000}{12000})=P(z>2.33)

P(z>2.33)=1-P(Z

Sicne this probability just represent 1% of the data we can consider this value as unusual.

d) z=1.28

And if we solve for a we got

a=72000 +1.28*12000=87360

So the value of height that separates the bottom 90% of data from the top 10% is 87360.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the life of a particular auto transmission of a population, and for this case we know the distribution for X is given by:

X \sim N(72000,12000)  

Where \mu=72000 and \sigma=12000

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability using excel or the normal standard table and we got:

P(z

Part b

P(X>65000)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>65000)=P(\frac{X-\mu}{\sigma}>\frac{65000-\mu}{\sigma})=P(Z>\frac{65000-72000}{12000})=P(z>-0.583)

And we can find this probability using the complement rule and excel or the normal standard table and we got:

P(z>-0.583)=1-P(Z

Part c

P(X>100000)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>100000)=P(\frac{X-\mu}{\sigma}>\frac{100000-\mu}{\sigma})=P(Z>\frac{100000-72000}{12000})=P(z>2.33)

And we can find this probability using the complement rule and excel or the normal standard table and we got:

P(z>2.33)=1-P(Z

Sicne this probability just represent 1% of the data we can consider this value as unusual.

Part d

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.1   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=1.28

And if we solve for a we got

a=72000 +1.28*12000=87360

So the value of height that separates the bottom 90% of data from the top 10% is 87360.  

You might be interested in
The ages in years of eight boys are 14,
SashulF [63]

Answer:

B) 13

Step-by-step explanation:

Average age means to calculate mean:

Mean = (Sum of all numbers)/(Number of numbers)

Mean = (14 + 14.5 + 12 + 11.5 + 15 + 13 + 10.5 + 13.5)/8

Mean = (104)/8

Mean = 13

5 0
3 years ago
I roll a four-sided die. The possible outcomes are 1, 2, 3, or 4, depending on the number ot spots on the side of the die that i
Daniel [21]

Answer:

The sample space

Step-by-step explanation:

By definition, the sample space is the set composed by all the possible outcomes of your random variable. In this case, the random variable is 4 sided dice, so the sample space is

\Omega=\{1,2,3,4\}

8 0
3 years ago
My sister went QUaCk and my heart QuaKeD
labwork [276]

Answer:

That's nice

But it should've YEETED

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Solve for x. show your work.​
vova2212 [387]

Hello!

\large\boxed{x = 8}

The two angles pictured are corresponding angles, so they are congruent.

Therefore:

17x - 4 = 12 + 15x

Isolate for x by subtracting 15x from both sides:

2x - 4 = 12

Add 4 to both sides:

2x = 16

Divide both sides by 2:

x = 8.

5 0
3 years ago
Read 2 more answers
What is the approximate percent decrease from 1,865 to 1,240?
bearhunter [10]

Answer: 33.5

Step-by-step explanation: this question is on brainly lol but nobody explained it

1865 - 1240 = 625

Divide 625 by 1865 (626 goes first)

The answer is 0.335 move the decimal 2x forward

33.5

4 0
3 years ago
Read 2 more answers
Other questions:
  • A spinner with 4 colors is spun for a total of 50 trials. Yellow was selected 10 times. What is the experimental probability of
    9·2 answers
  • Which of the following would have a scale factor with an absolute value greater than 1?
    13·1 answer
  • X + 2y = 8<br> X + 3y = 12
    7·1 answer
  • What is x equal to ?
    8·1 answer
  • Jillian tracks her progress on her spelling test over a period
    14·2 answers
  • le Gianna just started a running plan where she runs 20 miles the first week and then increases the number of miles she runs by
    7·1 answer
  • Die m-my dinosaur nuggys are gone ​
    11·1 answer
  • on Monday 76 students played soccer on Tuesday 62 students play soccer on Wednesday 68 students play soccer how many more studen
    6·1 answer
  • Robert is building a deck in his backyard. Each piece of wood measures 42.5 inches. If he has 86 boards, how long are they altog
    10·1 answer
  • | Solve for X<br> 8x + 1 = 49
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!