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
Plzz help me im giving 12 points
Serggg [28]
This Is very simple.

30m + 50 = 20m + 100

This is the new equation needed to solve for m.
first we must isolate "m".

30m + 50 = 20m + 100
        - 50             - 50

30m = 20m + 50
-20m   -20m

10m = 50

divide both sides by 10 to isolate "m".

m = 5

hope this helps!





3 0
3 years ago
Factor completely, then place the factors in the proper location on the grid.
Lyrx [107]
4(x+5y)(x-3y)
I don't know what you mean by placing the factors on the grid
6 0
3 years ago
Geraldine is picking a four-digit password by using the digits 0 through 9. She can use each digit only once. How many different
BabaBlast [244]

Answer:

5040 different combinations

Step-by-step explanation:

0-9 = 10 numbers

1st digit can be 1 0f 10

2nd digit can be 1 of 9

3rd digit can be 1 of 8

4th digit can be 1 of 7

10×9×8×7=5040

5 0
3 years ago
Read 2 more answers
WILL MARK BRANLIEST!!!!!! HELP ASAP!!
lubasha [3.4K]

Answer:

5 11/36

Step-by-step explanation:

7 0
3 years ago
What is z to the -6th power
jeka94

Answer:

  • z^(-6) or  1/z^6

Step-by-step explanation:

What is z to the -6th power?

  • z^(-6) = 1/z^6
4 0
2 years ago
Other questions:
  • PLEASE HELP!
    8·1 answer
  • Which role would result in a translation of two units left and three units up
    12·1 answer
  • Find the value of x.
    9·1 answer
  • Trig please help
    6·1 answer
  • Someone help with this please
    8·1 answer
  • The two triangles below are congruent. Which of the following are congruent by CPCTC?
    15·2 answers
  • Emmet rolls a number cube. In 5 out of 24 trials, he rolls a six. What is the
    7·1 answer
  • The total cost of renting a banquet hall is a function of the number of hours the
    11·1 answer
  • Find the new amount given the original amount and the percent of change.
    5·1 answer
  • 8x-3y times 5x5y over 10x6y2
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!