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
Zarrin [17]
3 years ago
11

The mean output of a certain type of amplifier is 183 watts with a variance of 121. If 78 amplifiers are sampled, what is the pr

obability that the mean of the sample would differ from the population mean by less than 1.7 watts? Round your answer to four decimal places.
Mathematics
1 answer:
koban [17]3 years ago
4 0

Answer:

0.8278 = 82.78% probability that the mean of the sample would differ from the population mean by less than 1.7 watts

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(which is the square root of the variance) \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 normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}};

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 183, \sigma = \sqrt{121} = 11, n = 78, s = \frac{11}{\sqrt{78}} = 1.2455

Probability that the mean of the sample would differ from the population mean by less than 1.7 watts?

This is the pvalue of Z when X = 183+1.7 =184.7 subtracted by the pvalue of Z when X = 183 - 1.7 = 181.3.

X = 184.7

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

By the Central Limit Theorem

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

Z = \frac{184.7 - 183}{1.2455}

Z = 1.365

Z = 1.365 has a pvalue of 0.9139

X = 181.3

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

Z = \frac{181.3 - 183}{1.2455}

Z = -1.365

Z = -1.365 has a pvalue of 0.0861

0.9139 - 0.0861 = 0.8278

0.8278 = 82.78% probability that the mean of the sample would differ from the population mean by less than 1.7 watts

You might be interested in
WI MARK AS BRAINLIAST!! 20PTS!! PLS HELP ASAP!!!​
earnstyle [38]

Answer:

14. 118

15. 28

16. 152

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Rearrange f=3g+2 to make g the subject
Helen [10]
Minus 2 from bothsides
f-2=3g
divide both sides by 3
(f-2)/3=g
g=(f-2)/3
6 0
3 years ago
Read 2 more answers
A(c−b)=d solve for c
Rainbow [258]

Answer:

The solution to this equation could not be determined.

Step-by-step explanation:

Simplifying

a(c + -1b) = d

Reorder the terms:

a(-1b + c) = d

(-1b * a + c * a) = d

(-1ab + ac) = d

Solving

-1ab + ac = d

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Combine like terms: d + -1d = 0

-1ab + ac + -1d = 0

The solution to this equation could not be determined.

4 0
3 years ago
The interest rate r required to increase your investment p to the amount a in t years is found by mc075-1.jpg. Find the interest
kotegsom [21]
I hope this is the answer :)
45.67=r

6 0
3 years ago
Read 2 more answers
In an election, 471 people voted. Candidate B received 2/3 of the votes. How many votes did Candidate B receive?
dezoksy [38]

Answer:

Step-by-step explanation:

471/3 * 2 = 314

5 0
3 years ago
Read 2 more answers
Other questions:
  • Find the cosine of the angle between the planes 4x−1y+2z=−4 and the plane 1x+1y−4z=3.
    9·1 answer
  • If it were possible to eat a hamburger every minute of every day without stopping how many years would it take to eat a billion
    11·1 answer
  • Help me with this please
    11·1 answer
  • Simplify the expression and find its value: (2x+0.5)^2–(2x–0.5)^2 for x=−3.5
    5·1 answer
  • - For any nonquadrantal angle 0, sin 0 and csc 0 will have the same sign explain why
    9·1 answer
  • Jessica and her friends have gone to dinner. When they finished eating their bill came to $82. Jessica decided that she wanted t
    9·2 answers
  • A basket ball player attempts 15 baskets in a game . He makes 9 of the attemps what is the ratio
    6·1 answer
  • Given that the measure of angle 3 is 75o. What is the value of x if the measure of angle 7 is (x + 40) ?
    10·2 answers
  • Pls helo me with this pls
    11·1 answer
  • If a die is rolled it may have 1, 2, 3, 4, 5, or 6 showing, and each outcome is equally likely to occur. If three dice are rolle
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!