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
nirvana33 [79]
3 years ago
5

The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a mean of 60,000 miles and

a standard deviation of 4,000 miles. Suppose you bought a set of four tires, what is the likelihood the mean tire life of these four tires is between 57,000 and 63,000 miles
Mathematics
1 answer:
egoroff_w [7]3 years ago
4 0

Answer:

86.64% probability that the mean tire life of these four tires is between 57,000 and 63,000 miles

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 60000, \sigma = 4000, n = 4, s = \frac{4000}{\sqrt{4}} = 2000

Suppose you bought a set of four tires, what is the likelihood the mean tire life of these four tires is between 57,000 and 63,000 miles

This is the pvalue of Z when X = 63000 subtracted by the pvalue of Z when X = 57000. So

X = 63000

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{63000 - 60000}{2000}

Z = 1.5

Z = 1.5 has a pvalue of 0.9332

X = 57000

Z = \frac{X - \mu}{s}

Z = \frac{57000 - 60000}{2000}

Z = -1.5

Z = -1.5 has a pvalue of 0.0668

0.9332 - 0.0668 = 0.8664

86.64% probability that the mean tire life of these four tires is between 57,000 and 63,000 miles

You might be interested in
The area of a square is 64 square units. How many units long is each of its sides?
skelet666 [1.2K]
<h2>Area of a square = side × side</h2>

Let the side = x

{x}^{2}  = 64 \\ x =  \sqrt{64}  \\ x = 8

<h3>Length of each side = <u>8</u><u> </u><u>units</u></h3>

.... Hope this will help....

3 0
2 years ago
B) Tyler swam 32 laps in the pool. Kevin swam 3 times as many laps as Tyler. Lets the number of
evablogger [386]

If Tyler did 32 laps and Kevin did 3 times that amount; its quite simple, you would find three times the amount of Tylers laps which is 96.

4 0
2 years ago
Read 2 more answers
What happens when the scale factor is negative?
Anastaziya [24]
That menas that it we be negative because any thing that is negative is going bigger 
7 0
3 years ago
Read 2 more answers
Use the equation below to find y, if m= 8 and x=6.<br> y=mx <br> y=?
Lunna [17]

Answer:

The value of y is 48.

Step-by-step explanation:

You have to substitute the values into the equation :

y = mx

let \: m = 8,x = 6

y = 8 \times 6

y = 48

8 0
2 years ago
Read 2 more answers
the standard addition algorithm below is being used to add three two-digit numbers 4z + 27 + x 5 equals y 14. If x, y, and z eac
Studentka2010 [4]
For the units positions of all numbers we have:
z+7+5=4 \\ z+12=4
From this we can conclude that total sum of these three numbers is 14. Number 1 we carry to next step. So we have:
z+12=14 \\ z=2

For the tens positions of all numbers we have:
4+2+x+1=1 \\ 7+x=1
The extra number 1 on left side comes from the carry from last step. Similar to ones position we know that total sum is 11.
7+x=11 \\ x=4

Now we insert x and z to find out y:
42+27+45=y14 \\ 114=y14 \\ y=1

Now we need to find out the product of these three numbers:
x*y*z=4*1*2=8
3 0
3 years ago
Other questions:
  • A manufacturing company produces valves in various sizes and shapes. One particular valve plate is supposed to have a tensile st
    15·1 answer
  • Evaluate the function f(x)=x+4 when x=3.
    6·1 answer
  • Kia wants to have 3 pounds of munchies for her party. She has 20 ounces of popcorn and wants the rest to be pretzel sticks. How
    13·1 answer
  • Are the brackets correct
    15·2 answers
  • Jenny rented a bike from Danielle's Bikes.
    13·2 answers
  • Which fraction is equivalent to 2/6?
    15·1 answer
  • In a biconditional statement, the output is true if at least one input is true.
    11·1 answer
  • Simplify -5x(x - 3y)
    7·1 answer
  • Show your work on this I will mark as brainliest as well
    12·2 answers
  • Simplify the radical expression
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!