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
Can someone help me please
valina [46]

Answer:

It's 28

Step-by-step explanation

7 0
3 years ago
The function h(t) = 210 – 15t models the altitude of a hot air balloon over time t, in minutes.
Firdavs [7]
H(10)=210-15(10)
h(10)=210-150
h(10)=60

The hot air balloon is at an altitude of 210. The hot air balloon slowly falls 15 () per minute, for 10 minutes. He ends up at 60 altitude
6 0
3 years ago
2 1/2 x 3 1/5 fast please
vova2212 [387]

Step-by-step explanation:

<u>Let's turn each mixed fraction into an improper fraction:</u>

2 \frac{1}{2} =\frac{2}{2} +\frac{2}{2} +\frac{1}{2} =\frac{5}{2}

3\frac{1}{5} =\frac{5}{5} +\frac{5}{5} +\frac{5}{5} +\frac{1}{5} =\frac{16}{5}

<u>Multiply:</u>

\frac{5}{2} \times \frac{16}{5} =\frac{80}{10}

<u>Simplify:</u>

\frac{80 \div 10}{10 \div 10} =\frac{8}{1} =8

8 is your simplified product.

4 0
3 years ago
isabella bought one chocolate pie for 88 cents and one cookie for 65 cents. how much did isabella spend ?
QveST [7]
153 cents or $1.53 sorry if I'm wrong
8 0
3 years ago
Read 2 more answers
Help with this one? Please
netineya [11]

Answer:

x = 40

Step-by-step explanation:

The figure shows two similar triangles. Thus, the side lengths of similar triangles are proportional to each other. Therefore:

\frac{24}{24 - 15} = \frac{x}{x - 25}

\frac{24}{9} = \frac{x}{x - 25}

Cross multiply

24(x - 25) = 9(x)

24x - 600 = 9x

Subtract 24x from each side

- 600 = 9x - 24x

- 600 = -15x

Divide both sides by -15

40 = x

x = 40

3 0
2 years ago
Other questions:
  • Graph the function and identify the domain and range y= -4 x^2
    8·1 answer
  • Make up any kimd of subtraction equation thay has a solution of -2​
    11·1 answer
  • U need help ASP .<br>f(x)=1-3X and g (x)=x+4 calculate gf(-2)<br>​
    11·1 answer
  • On sale for 25% of the retail price.
    7·1 answer
  • debby collected eight times as many bags of cans as her friend. if her friend collected 1 2/3 pf bags. how many did debby collec
    14·1 answer
  • PLEASE HELP NOW WILL MARK BRAINLEST FOR CORRECT ANSWER A Brazilian town near the Amazon River has experienced 7% annual decrease
    11·2 answers
  • What is the value of the function y=3x-1 when x = –1?<br> a. –8<br> b. –4<br> c. 2<br> d. 6?
    5·1 answer
  • Solve 6- 7x = 7x - 9x + 11 The value of xis​
    10·1 answer
  • The cost of renting a truck is $40. An additional $0.79 is charged for each mile, m, the truck is driven. Which expression can b
    7·1 answer
  • Elouise is creating a rectangular garden in her backyard. The length of the garden is 12 feet. The perimeter of the garden must
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!