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
Zina [86]
3 years ago
10

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 48,564 miles, with a standard

deviation of 3293 miles. What is the probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct? Round your answer to four decimal places.
Mathematics
1 answer:
DerKrebs [107]3 years ago
6 0

Answer:

0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct

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 = 48564, \sigma = 3293, n = 281, s = \frac{3293}{\sqrt{281}} = 196.44

What is the probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct?

This is the pvalue of Z when X = 48101. So

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

By the Central Limit Theorem

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

Z = \frac{48101 - 48564}{196.44}

Z = -2.36

Z = -2.36 has a pvalue of 0.0091

0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct

You might be interested in
Guys, I’m giving you at least 100 points for you to answer to my angles, triangles, and quadrilaterals word problem homework pac
frez [133]

Step-by-step explanation:

For question 22: Notice the congruent symbol on sides AB and CB; this shows that the triangle is isosceles, and in an isosceles triangle, the angles opposite congruent sides are congruent. Thus, angle A actually equals angle C.

In other the find B, it is know that all of the interior angles of a triangle must add to 180; thus, this can be written as: angle A + angle B + angle C = 180.

Since you already know angles A and C, subtract angle A and angle C from 180 to get angle B.

For question 23:

Notice that triangle DBC is an isosceles triangle, and that angle D and angle C are opposite of congruent sides, indicating that they are equal. Since the interior angles of a triangle must add up to 180, and you know that angle D equals angle C, you can find angle DBC by doing 180 - (2 * angle D).

Now that you have angle DBC, you can find angle CBA; since these two angles form a straight line, you know they must add to 180 degrees. Thus, 180 - angle DBC equals angle CBA.

Now, notice that triangle CBA is also isosceles, and that angles CBA and angle A are opposite congruent sides, indicating that they are also congruent. Thus, angle A equals angle CBA.

Hope this helps :)

4 0
2 years ago
Which of the following is the correct value for x
USPshnik [31]
(1) 5 is the answer
7 0
3 years ago
I need help with this math
Zinaida [17]

Answer:

D

Step-by-step explanation:

∠1 + ∠2  =  180   {Supplementary angles}

6x + 15 + 3x + 3 = 180

6x + 3x + 15 + 3 = 180      

Combine like terms

9x + 18 = 180

Subtract 18 from both sides

9x = 180 - 18

9x = 162

x = 162/9

x = 18

∠2 = 3x +3

     = 3*18 + 3

     = 54 + 3

∠2 = 57°

8 0
2 years ago
Read 2 more answers
Which is the graph of f(x) = 2(3)x
hammer [34]
The graph of f(x)=2(3)x would look like this

7 0
3 years ago
Find the range 7,6,5,9,5,8,2 please include work!!
ArbitrLikvidat [17]

Answer:

7.

Step-by-step explanation:

Range = highest value - lowest

= 9 - 2

= 7.

5 0
3 years ago
Other questions:
  • A lawn sprinkler spins in a circle. The sprinkler covers a radius of 4 feet. Which choice is the closest to the area of lawn tha
    6·2 answers
  • HELP PLEASE <br><br><br> FIND THE VALUE OF THE FOLLOWING EXPRESSION
    12·1 answer
  • a seafood company sold 9,125 pounds of fish last month. if 6 seafood companies sold the same amount of fish how much fish did th
    12·2 answers
  • If g(x) is the graph of f(x) shifted up 5 units and right 1 units, write formula for g(x)
    9·1 answer
  • For the following distribution:
    11·1 answer
  • Hey, I’m new to this app i download the app today, and i hope if is there people who can help me with this question in the pictu
    10·1 answer
  • Find a value for a that makes this statement true.<br><br> a ÷ 6 greater than 1.
    15·2 answers
  • Can you help me with this question?​
    5·1 answer
  • Important, help asap
    11·1 answer
  • Rename 1/10 and 1/4 <br> using the least common denominator.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!