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
Delvig [45]
3 years ago
14

"A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean

is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.1 hours."
Mathematics
1 answer:
Arada [10]3 years ago
4 0

Answer:

85.31% probability that their mean rebuild time exceeds 8.1 hours.

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 are 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 = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846

If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.1 hours.

This is 1 subtracted by the pvalue of Z when X = 8.1. So

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

By the Central Limit Theorem

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

Z = \frac{8.1 - 8.4}{0.2846}

Z = -1.05

Z = -1.05 has a pvalue of 0.1469

1 - 0.1469 = 0.8531

85.31% probability that their mean rebuild time exceeds 8.1 hours.

You might be interested in
How to do you find the constant of variation when it’s a direct variation?
ololo11 [35]

Answer:

The constant of variation in a direct variation is the constant (unchanged) ratio of two variable quantities. The formula for direct variation is. y = k x (or y = k x ) where k is the constant of variation . Example 1: If y varies directly as x and y = 15 when x = 24 , find x when y = 25 .

Step-by-step explanation:

Hope this helps, mark brainliest

3 0
2 years ago
I’m putting the right answer which is “6” but the computer keeps telling me I’m wrong, I don’t understand, what else is there to
iragen [17]

You may have have forgotten to find the measure of A. Which would by using your 6 that you got would be 19.  

16X-6=90

96=16X

X=6

8X6-29

48-29

19

3 0
2 years ago
A teacher has 100 chairs to arrange for an assembly into equal rows Write one way the chairs could be arranged Include the numbe
tiny-mole [99]
That's easy if there is 100 chairs there would be 10 rows with ten chairs in each row
3 0
3 years ago
Read 2 more answers
You have prizes to reveal! Go to<br> Does (7,9) make the inequality 15x + 17y &gt; 13 true?
Hoochie [10]

Answer:

yes it is cause the answers 258

3 0
3 years ago
Read 2 more answers
15) 3x2 y4 z − 6xy − 3z(5x2) How many terms are in the expression?
klio [65]
Ok name the expressions we both know 3z is one 5x is one 6xy is one do you think 3x^2y^4z is an expression i would give you the answer but i also want you to understand the problem and what your looking for to in the equation
6 0
3 years ago
Other questions:
  • Whats 50 times 40 ??????????
    8·2 answers
  • 600+15y=750.<br> solve for y<br> can I as well have the way you solved for y?
    15·2 answers
  • Monday: 10 apples and 5 bananas cost £4.20 Friday: 8 apples and 10 bananas cost £5.40 Find the cost of each - with an explanatio
    9·1 answer
  • Graph the solution set of x &lt; -8
    6·1 answer
  • What is the Value of X?<br> 8<br> 10<br> 13<br> 20
    5·2 answers
  • Order the following numbers from least to greatest. Put the lowest number on the left. 2 -2 5 -5
    6·1 answer
  • Which operation should you perform first when you simplify the following (15 x 5 + 4) x 3
    9·2 answers
  • Help please!!
    10·1 answer
  • FR.EE POI.NTS!!!!!!!! I HOPE U HAVE/HAD A NICE DAY OR NIGHT
    9·1 answer
  • Suppose 2' is a normally distributed random variable with ft = 10.3 and 0 = 3.8. For the following probability,draw an appropria
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!