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
Write the expression that represents 7 subtracted from 8n.
kicyunya [14]
I think it's B.............
3 0
2 years ago
Read 2 more answers
How can you make 19 out of 10 8 5 2 3
postnew [5]
8-2=6
10+6+3=19

I’m not sure if you are allowed to do it that way so I can find other ways if needed
7 0
2 years ago
Read 2 more answers
Will mark as brainliest! 40 points! Thanks!
n200080 [17]

When given a system of equations, the "solutions" are defined where two equations intersect, or meet.


A. The point where the lines p(x) and g(x) meet is (3, -1), and thus this is considered the solution set.

B. Because there are three lines in total, g(x) is able to intersect both lines one time, and so it has two pairs of solutions.

The first is (3, -1), which has already been established with p(x).

The second is (0, 5), and this is where it intersects with f(x).

C. The solution to f(x) = g(x) is 0, as this is the only x value where both equations are equal.


Hope my answer helped!

6 0
2 years ago
Read 2 more answers
Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
Harman [31]

Formula for the perimeter of a quarter circle: C = ((pi x 2r) / 4) + 2r

C = ((3.14 x 18) / 4) + 18

C = (56.52 / 4) + 18

C = 14.13 + 18

C = 32.13 miles

Hope this helps! :)

5 0
3 years ago
A city's population is 12,000 and grows at 2.6% rate. What will the population be after 25 years? A city's population is 230,000
Levart [38]

Answer:

The 12000 City would become 22,986 people, while the 230,000 city would become a population of 124,223.

Step-by-step explanation:

1st Part:

=12000⋅(0.026000000000000002⋅25)

=12000(2.718281828459045)(0.65)

=22986

2nd Part:

=230000⋅(−0.044000000000000004⋅14)

=230000(2.718281828459045)(−0.616)

=124223

3 0
2 years ago
Read 2 more answers
Other questions:
  • Mr. Morgan has five daughters. They were all born the number of years apart as the youngest daughter is old. The oldest daughter
    7·2 answers
  • Find x so that m || n.
    8·1 answer
  • Triangle RSU is an equilateral triangle. RT bisects US. Find x and y. (y+12)°
    11·1 answer
  • Express the polynomial 2m^2-3+7m in standard form
    14·1 answer
  • Wich of the following is an example of a Proper fraction? A.4/17 B.15/2 C.6/6 D.11/10/
    9·1 answer
  • What is the median of the data set? <br><br> {16, 15, 17, 19, 12, 11, 14, 14, 13, 11, 18, 15}
    6·2 answers
  • 5(×+y+4) is equivalent to what
    12·1 answer
  • Martha rolls a 6 sided number cube two times.
    12·1 answer
  • PLS PLS HELP HELP ME ITS EASY ITS FREE PONTS LOL PLS PLS HELP HELP ME ITS EASY ITS FREE PONTS LOL PLS PLS HELP HELP ME ITS EASY
    8·2 answers
  • What does x equal in this y=2x + 3
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!