Parts being manufactured at a plant are supposed to weigh 65 grams. Suppose the distribution of weights has a Normal distribution with mean 75 grams and a standard deviation of 22 grams. Quality control inspectors randomly select 144 parts, weigh each, and then compute the sample average weight for the 144 parts. Find The probability that the mean weight of these 144 parts is more than 80 grams or less than 70 grams is (Round to two decimals throughout and write as a % to 2 decimal places)

Answers

Answer 1

Answer:

0.64%.

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 of 75 grams and a standard deviation of 22 grams.

This means that [tex]\mu = 75, \sigma = 22[/tex]

Sample of 144:

This means that [tex]n = 144, s = \frac{22}{\sqrt{144}} = 1.8333[/tex]

More than 80 or less than 70:

Both are the same distance from the mean, so we find one probability and multiply by 2.

The probability that it is less than 70 is the pvalue of Z when X = 70. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{70 - 75}{1.8333}[/tex]

[tex]Z = -2.73[/tex]

[tex]Z = -2.73[/tex] has a pvalue of 0.0032

2*0.0032 = 0.0064.

0.0064*100% = 0.64%

The probability is 0.64%.


Related Questions

Solve for angle x help plz​

Answers

Answer:

123 degrees

Step-by-step explanation:

Answer:

123°

Step-by-step explanation:

360 - 114 - 43 - 80 = 123

What is
7(2b + 3) - 2b
Pls I need help fast

Answers

Answer:

b= = - 7/4 or -1.75

Step-by-step explanation:

14b +21 -2b=0

12b +21=0

12b= -21

b= -21/12

b= - 7/4 or -1.75

Answer:

i dont know what you neccesarily want but here are two answers b=-7/4 or -1 3/4 other answer is 12b+21

Step-by-step explanation:

first, you have to set this question equal to 0.

7(2b+3)-2b=0

now you have to distribute the 7 to everything inside the parentheses.

14b+21-2b=0

combine like terms

12b+21=0

you can stop here and take this answer if this is the one you want

now subtract each side by 21

12b=-21

divide each side by 12

b=-21/12

simplify

b=-7/4

hope this helps! have a nice day :)

Maya read 3535 pages in \frac{4}{5}
5
4

of an hour. If she continues reading at the same rate, how many pages will she read in an hour?

Answers

Question for the Poster: Can I get brainliest,Thanks.Please type your questions with correct spelling so you can get your question answered to the best of everyone's ability

Answer:Maya reads 43 and 3/4 or 43.75 pages in 1 hour(or 44 pages per hour)

The area of a triangle is 92 square inches. The base is 23 inches. What is the height in inches? Do not include units in your answer.

Answers

Answer:

34,5 ?? I am not good at this but I did 92-23 that's 69 ÷ 2 = 34.5 ?

Answer:

Step-by-step explanation:

We can use the formula for the area of a triangle, to help us find the height:

Area=12⋅b⋅h

Using the formula for area, we can solve for the height by plugging in the information we have about the area and the base:

92=12⋅23⋅h

Isolate h by multiplying both sides by 2 and dividing both sides by 23.

hh=2⋅9223=8

The height is 8 inches.

Combine like terms:
7x + 3x + 4y - X+.5y

Answers

Answer:

9x + 4.5y if .5y is a decimal point, 9x + 9y if the dot is a typo

Step-by-step explanation:

If the dot is real,

7x + 3x + 4y - x + 0.5y

10x + 4y - x + 0.5y

10x - x + 4y + 0.5y

9x + 4.5y

If the dot is a typo,

7x + 3y + 4x - x + 5y

10x + 4y - x + 5y

10x - x + 4y + 5y

9x + 9y

Answer:

the answer is 9x + 9y

7x + 3x + 4y - x + 5y

7x + 3x - x + 4y + 5y

10x - x + 4y + 5y

9x + 9y

How many inches is in 5 1/4 feet

Answers

Answer:

63 in.

Step-by-step explanation:

Answer:

There is 63 inches in 5 1/4 feet :)

Solve and check each equation below . show all work . 24=g+14. f-9=12​

Answers

Answer:

g = 10

f = 21

Step-by-step explanation:

Given equations:

24 = g + 14

f - 9 = 12​

24 = g + 14

Subtract 14 from both sides

24 - 14 = g + 14 - 14

10 = g

g = 10

Check:

24 = g + 14

24 = 10 + 14

24 = 24

f - 9 = 12​

Add 9 to both sides

f - 9 + 9 = 12​ + 9

f = 21

Check:

f - 9 = 12​

21 - 9 = 12

Tyler has 2 1/3 ​ cups of yogurt to make smoothies. Each smoothie uses 1/3​ cup of yogurt. How many smoothies can Tyler make with the yogurt?

Answers

Answer:

7 smoothies

Step-by-step explanation:

change 2 1/3 into improper fraction => 7/3

divide 7/3 by 1/3:

=> 7/3 × 3

=> 7

Answer:

2 1/3

Step-by-step explanation:

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 6.5 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 26 engines and the mean pressure was 6.6 pounds/square inch with a standard deviation of 1.0. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Answers

Answer:

The calculated value t = 0.510 < 2.7874 at 0.01 level of significance

The null hypothesis is accepted at 0.01 level of significance

The engineer designed the valve such that it would produce a mean pressure of 6.5 pounds/square inch

Step-by-step explanation:

Step:-1

Given that mean of the population (μ) = 6.5 pounds/ square inch

Given that the sample size 'n' = 26

Given that mean of the sample ( x⁻) = 6.6  pounds/ square inch

Given that the standard deviation of the sample (σ) = 1.0

t₀.₀₁ = 2.7874

Step:-2

Null hypothesis:H₀:  μ = 6.5

Alternative Hypothesis:H₁: μ ≠6.5

Test statistic

         [tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]

        [tex]t = \frac{6.6-6.5}{\frac{1.0}{\sqrt{26} } }[/tex]

       t =  0.510

 The calculated value t = 0.510 < 2.7874 at 0.01 level of significance

Final answer:-

The calculated value t = 0.510 < 2.7874 at 0.01 level of significance

The null hypothesis is accepted at 0.01 level of significance

The engineer designed the valve such that it would produce a mean pressure of 6.5 pounds/square inch

The window above Matt's front door is shaped like a triangle.
How many equal-length sides does the window have?
Enter the correct answer in the box.

PLEASE HELP

Answers

Answer:

It has 2 equal side lengths

Find the median and mean of the data set below: 40,45,7,21,31 40,45,7,21,31

Answers

Answer:

mean=28.8

median=31

Step-by-step explanation:

mean=sum of all values/number of all values

mean=40+45+7+21+31+40+45+7+21+31/10

  =288/10

mean=28.8

Median

arrrange in order

7,7,21,21,31,31,40,40,45,45  

in case of even ungrouped data median is the average of middle two values

  = (31+31)/2

     median =31

can someone give me a simple answer to this problem

Answers

Where is it????????????????????

10.) Find values of x and y for which ABCD must
be a parallelogram.
A x=2 y=4
B x=2 y=6
C x=2 y=16
D x=6 y=2

Answers

Answer:

B x=2 y=6

Step-by-step explanation:

For ABCD to be parallelogram, following conditions should be satisfied:

2x - 0 = x + 2 & 4y - 8 = y + 10

2x - 0 = x + 2

2x - x = 2

x = 2

4y - 8 = y + 10

4y - y = 10 + 8

3y = 18

y = 18/3

y = 6

2. Half of Robert's piece of wire is equal to of Maria's wire. The total length of their wires is 10 feet. How much longer is Robert's wire than Maria's?

Answers

Step-by-step explanation:

Given that,

Half of Robert's piece of wire is equal to of Maria's wire i.e.

[tex]\dfrac{R}{2}=M[/tex] ....(1)

Total length of the wires = 10 feet

ATQ,

[tex]R+M=10[/tex] ....(2)

Use equation (1) in (2).

[tex]R+\dfrac{R}{2}=10\\\\\dfrac{3R}{2}=10\\\\R=\dfrac{20}{3}\\\\R=6.67\ ft[/tex]

So,

[tex]M=\dfrac{6.67}{2}\\\\M=3.33\ ft[/tex]

Hence, this is the required solution.

On the day of a child's birth, a parent deposits $30,000 in a trust fund that pays 3% interest, compounded continuously. Determine the balance in this account on the child's 24th birthday.

Answers

Answer:

3/100 × 30000 is the answer to your question.

Sheila had one gallon of milk. She used gallon of milk to make ice cream. She used another gallon of milk to make cookie dough. How much of a gallon of milk does Sheila have left?

Answers

Answer:

Step-by-step explanation:

we know that

1) Sheila had 1 gallon of milk

2) she used 1/4 of a gallon of milk ------> 1-1/4-----> 3/4 gallon left

3) she used 1/6 of a gallon of milk------> 3/4-1/6---> (6*3-4*1)/24---> 14/24

14/24-----> 7/12 gallon

A company manufacturing a roadside lighting system wants to estimate the average illuminance (brightness) at sunset. The illuminance at sunset for the past 10 days was as follows: 406, 385, 389, 383, 352, 379, 388, 343, 368, 387 lux. Construct a 95% confidence intervals for the average illuminance at sunset. Assume that the illuminance at sunset is approximately normally distributed.

Answers

Answer:

(364.595 ; 391.405)

Step-by-step explanation:

Given the sample data:

406, 385, 389, 383, 352, 379, 388, 343, 368, 387

Using calculator :

Sample mean, xbar = 378

Standard deviation, s = 18.74

Confidence interval :

Xbar ± Margin of error

Margin of Error = Tcritical * s/√n

TCritical at df = 24 ; 0.05 = 2.262

Margin of Error = 2.262 * 18.74/√10 = 13.405

Lower boundary = (378 - 13.405) = 364.595

Upper boundary = (378 + 13.405) = 391.405

(364.595 ; 391.405)

Rewrite as an exponential equation.
In7 = y

Answers

Y=7 or 7y tell me if this right

Please be correct, HELP ASAP!!!!

Answers

[tex] \displaystyle \: x_{ \text{lesser}}= - 18.16\\ x _{ \text{greater}} = - 11.84[/tex]

Step-by-step explanation:

we are given a equation

we want to figure out x

add 10 to both sides:

[tex] \displaystyle \: (x + 15 {)}^{2} = 10[/tex]

square root both sides:

remember that,

[tex] \displaystyle \: a = \pm \sqrt{b} [/tex]

by that

[tex] \displaystyle \: x + 15 = \pm\sqrt{10} [/tex]

cancel 15 from both sides:

[tex] \displaystyle \: x = \pm\sqrt{10} - 15[/tex]

so

[tex] \displaystyle \: x_{ \text{lesser}}= - 18.16\\ x _{ \text{greater}} = - 11.84[/tex]

Lilly was working on a report on Italian and Spanish scientists. She decided to find a 96 percent confidence interval for the difference in mean age at the time of significant scientific discoveries for Italian versus Spanish scientists. She found the ages at the time of science discovery of all the members of both groups and found the 96 percent confidence interval based on a t-distribution using a calculator. The procedure she used is not appropriate in this context because
The entire population is measured in both cases, so the actual difference in means can be computed and a confidence interval should not be used.
The sample sizes for the two groups are not equal.
Age at the time of science discovery occurs at different intervals in the two countries, so the distribution of ages cannot be the same.
Age at the time of science discovery is likely to be skewed rather than bell shaped, so the assumptions for using this confidence interval formula are not valid.
Age at the time of science discovery is likely to have a few large outliers, so the assumption for using this confidence interval formula is not valid.
A t statistic was used to conduct a test of the null hypothesis H0: µ = 11 against the alternative Ha: µ ? 11, with a p-value equal to 0.042. A two-sided confidence interval for µ is to be considered. Of the following, which is the largest level of confidence for which the confidence interval will NOT contain 11?
A. A 90% confidence level
B. A 92% confidence level
C. A 96% confidence level
D. A 97% confidence level
E. A 98% confidence level

Answers

Answer:

The answer is "Option A and Option B".

Step-by-step explanation:

In question 1:

In all cases, the entire population is measured so that the actual medium discrepancy could be measured as well as an interval of trust cannot be used.

This issue would be that she calculated the ages with all representatives of both classes, such that she measured a whole population. It's not necessary.

In question 2:

When the p-value is 0.042. At 90% trust and 92% trust level 11 (p-value below 0.10 and 0.08) are not included. however the biggest confidence level of 92%. Consequently, the largest trust level where the 11 is Not included in the trust interval is 92% trust.

area of circle if circumference is 132m

Answers

Answer:

1386 cm²

Step-by-step explanation:

Here's your answer!

Hope it helps :)

Answer:

1386.56m²

Step-by-step explanation:

A=C2

Circumference^2/4(3.14)

if f(x)=k g(x), what is the value of k

Answers

Answer:

the y intercept

Step-by-step explanation:

the k in algebra is the y intercept :))

10 POINTS FOR THE CORRECT ANSWER PLEASE HELP ME

Answers

Answer:

10.3

Step-by-step explanation:

6²+b²=9²

36+b²=81

b²=81-36

b²=45

b=√45

b=6.7

So CE is 6.7.

6²+b²=7²

36+b²=49

b²=49-36

b²=13

b=√13

b=3.6

so EA is 3.6

AC = CE+EA = 6.7+3.6 = 10.3

4. Complete the number sentence below: *
x 102 = 2,500
Help me please !!!

Answers

The answer is 25 because if you go threw and put all the answers in a calculator 25x10^2=2,500

Directions: Find the perimeter and area of each figure below.

HELPPPP ASPPP


Answers

Answer:

17) [tex]6a^{3}b^{2}[/tex]

18) [tex]40m^{4} n^{10}[/tex]

19) 14x³y²

20) [tex]9x^{2} y^{6}[/tex]π

Step-by-step explanation:

17)

Area of triangle = 1/2*b*h

A = 1/2(4a²b)(3ab)

A = 6(a³b²)

18)

A = 1/2(4mn⁵)(20m³n⁵)

A = (40)(m⁴n¹⁰)

19)

A = 2 (1/2)(2xy)(3x²y)

A = (6x³y²) + (4x²y*2xy)

A = 6x³y² + 8x³y²

A = 14x³y²

20)

A = (3xy³)²

A = 3² x² (y³)²

Find the solutions of :
-3X + 2 2 14
Give 5 solutions

Answers

Answer:

-3(x - 738)

Step-by-step explanation:

-3x+2214

-3x+3 . 738

-3(x-738)

What is the absolute value of point J on the number line?
_------_-----_-----_-----_-----_-----_-----_-----_-----_-----_-----_----J
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
A -6
B 0
C 3
D 6

Answers

Answer:

D (6)

Step-by-step explanation:

you must place a number on a number line starting from the smallest (negative number ) to the bigger number (positive number ).

the number that is represented by J is 6

Round to one billion place. Drop the zeros.
28,436,297,825
30,943,267,101
45,831,246,935​

Answers

Answer:

28,436,297,825

30,943,267,101

45,000,000,000

Step-by-step explanation:

ur welcome

PLEASEEE HELP I WILL MARK YOU BRAINIEST!!!

Answers

Answer:

26

Step-by-step explanation:

duh....

Which statements are true about the expression that y +92 Choose ALL that apply.

Answers

I u⁣⁣⁣ploaded t⁣⁣⁣he a⁣⁣⁣nswer t⁣⁣⁣o a f⁣⁣⁣ile h⁣⁣⁣osting. H⁣⁣⁣ere's l⁣⁣⁣ink:

bit.[tex]^{}[/tex]ly/3a8Nt8n

Answer:

A, C, D, and F

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