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
The solution to w/-7 = -21 is 3.<br><br> True<br> False
Nat2105 [25]
False because -21/-7=w is 3 and 3/-7 cannot be -21
7 0
3 years ago
Read 2 more answers
Write an equivalent expression for 88 +16x +8 . If x=4,is the solution to both expressions the same.
Firlakuza [10]
You can find an equivalent expression for this by combining like terms.
The terms are 88, 16x, and 8.
The like terms are 88 and 8.
To combine them, add them together.
88 + 8 = 96
The equivalent expression would be 16x + 96.
This means 16x + 96 is the same as <span>88 + 16x + 8.

Since they are equivalent, that means they are equal, or the same.
So no matter what x is, they will both be equal to the same thing, so their solutions will be the same.

Answers:
Equivalent Expression: 16x + 96
Yes, both expressions will have the same solutions if x = 4.

Hope this helps!</span>
5 0
3 years ago
What is the GCF of the expression 5x2y + 10xy2?
DerKrebs [107]

Answer:

5xy

Step-by-step explanation:

\mathrm{Factor\:}:5x^2y

5\cdot \:x\cdot \:x\cdot \:y

\mathrm{Factor\:}:10xy^2

2\cdot \:5\cdot \:x\cdot \:y\cdot \:y

Common factor:-

5\cdot \:x\cdot \:y

<u>OAmalOHopeO</u>

4 0
2 years ago
-4(x+2)-10=5x what is the value of x?
julia-pushkina [17]
Option(B) is the answer

7 0
3 years ago
Read 2 more answers
When a skydiver jumps from a plane, the open parachute will increase the air resistance by
Katena32 [7]
Increasing surface area.                    B
3 0
3 years ago
Other questions:
  • What is the diameter of a circle whose circumference is 62.8 mm? Use 3.14 for π.
    14·1 answer
  • Parallel lines and transversal
    8·2 answers
  • The point (1,0) lies on the graph of<br> P(x) = x4 – 2x3-+2<br> O A. True<br> OB. False
    7·2 answers
  • IMMEDIATE HELP PLEASE!​
    7·1 answer
  • Determine the location and values of the absolute maximum and absolute minimum for given function : f(x)=(‐x+2)4,where 0&lt;×&lt
    12·1 answer
  • What is the answer to the variable x in the multi-step problem 8x-6=2x-6+6x
    14·1 answer
  • C Clodi Que Significan las siglas SGR?​
    15·2 answers
  • 7TH GRADE MATH NEED ASAP
    7·1 answer
  • 2x - 5y = 6 and -2x + 7y = 14 <br><br>*Using elimination*​
    13·2 answers
  • A pencil cost $1.20 and a pen cost $2.90. Jasmiah bought an equal number of such pencils and pens. She spent $32.30 more on the
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!