An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 429 watts with a standard deviation of 10 watts. What is the probability that the mean amplifier output would be greater than 432.1 watts in a sample of 76 amplifiers if the claim is true

Answer:

0.0035 = 0.35% probability that the mean amplifier output would be greater than 432.1 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 normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, 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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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

Mean output of 429 watts with a standard deviation of 10 watts.

This means that [tex]\mu = 429, \sigma = 10[/tex]

Sample of 76:

This means that [tex]n = 76, s = \frac{10}{\sqrt{76}} = 1.147[/tex]

What is the probability that the mean amplifier output would be greater than 432.1 watts?

This is 1 subtracted by the pvalue of Z when X = 432.1. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{432.1 - 429}{1.147}[/tex]

[tex]Z = 2.7[/tex]

[tex]Z = 2.7[/tex] has a pvalue of 0.9965

1 - 0.9965 = 0.0035

0.0035 = 0.35% probability that the mean amplifier output would be greater than 432.1 watts.

Brainliest for correct answer, any inapplicable answer or absurd answer will be deleted and reported.

Solve by substitution the system of equations. (y = 4x + 1) (3x + 2y = 13).

Anna charges $8.50 per hour to babysit . How much will earn if she works for 31/2 hours?

find the area (pls help)

PLZ HELP!!!!! Find the slope of each line that passes through the given points. (−2, 1) and (6, −5)

You get your first job ever and they tell you that you will make $350.25 for 15 hours. How much money will you make working 40 hours?

PLS HELP answer all and the pictures, label them as the first 3, and the second one 4
1. Identify the solid by its description:
One triangular base and three lateral faces that are triangles
2. Identify the solid by its description:
Two parallel rectangular bases and four lateral faces that are rectangles

Amir has 5 cups of water. He uses it to water 12 plants. Each plant gets
the same amount of water. How much water does each plant get?

solve the equation of the 18y = 144 to find the value of y

The diameter of a circle is 16 kilometers. What is the angle measure of an arc 6​ kilometers long?
In simplest form

There are 5 slices in the pizza. Wayne ate 2 slices of the pizza. What fraction of the pizza is left?

Maximizing revenue. Edwards University wants to determine what price to charge for tickets to football games. At $18 per ticket, attendance averages 40,000 people per game. Every decrease of $3 to the ticket price adds 10,000 people to the average attendance. Every person at a game spends an average of $4.50 on concessions. What price per ticket will maximize revenue

Which two-way frequency table correctly shows the marginal frequencies?

When (3x + 2)^2 is subtracted from 10x^2, the result is

Billy ate 30% of a pizza and Bonnie ate 3/8 of a pizza who ate more

its very easy just try it

At the school fall festival, the student council sold sodas as a fundraiser. The table below shows the number of sodas they sold and the cumulative total money.

Sodas Sold Money Collected
0 $0.00
2 $3.00
5 $7.50
9 $13.50
10 $15.00

Based on the information, what is the price per soda?
A.
$1.50 per soda
B.
$0.50 per soda
C.
$2.25 per soda
D.
$2.50 per soda

HELP PLEAse?
Classify the triangle by its sides and angles.

-acute, scalene
-obtuse, scalene.
-acute, equilateral
-obtuse, equilateral

Jane's dog is 62 centimeters long. Alan's dog is 33 centimeters long. How
much shorter is Alan's dog than Jane's dog?

Find the measure of 44.
{
44
158°
K
*4 = [?]

n airline company charges the following baggage fees: $25 for the first bag and $35 for the second (i.e., you pay $60 if you check two bags). Suppose 54% of passengers have no checked luggage, 34% have one piece of checked luggage and 12% have two pieces. About how much revenue should the airline expect for a flight of 120 passengers

help help help please ​

Which is the cost of the minimum spanning tree of the weighted graph using Kruskal's Algorithm?

28
30
31
40

Warren reads 6 books each month as part of his book club. If Warren has read 24 books so
far, how many months has he been with his book club?

Determine which of the following pairs of angles are complementary,
supplementary or neither.

Show processes po Pa help po need ko po bukass pleaseeee po.... I BRAINLIEST ko po yung tamang sagot:(​

Is the following equation exponential? Why or why not y=x^2+5

Dont steal points please if you do you will get repo answer all please I will give brainliest if its correct and 5 stars rating and the heart thanks.

Can someone help with vectors?

Classify the triangle as acute, obtuse, or right based on the given side
lengths. *
3,4,6
Acute
Obtuse
Right