If you take a sample of 9 pacemakers from the company, what is the probability that the mean lifetime of components in this sample will be longer than 99 months

Answers

Answer 1

Using the normal distribution and the central limit theorem, it is found that there is a 0.9878 = 98.78% probability that the mean lifetime of components in this sample will be longer than 99 months.

In a normal distribution 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]

It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem:

The mean is of 9 years, hence, in months, [tex]\mu = 9(12) = 108[/tex]The standard deviation is of 1 year, hence, in months, [tex]\sigma = 12[/tex].Sample of 9 pacemakers, hence [tex]n = 9, s = \frac{12}{\sqrt{9}} = 4[/tex].

The probability is 1 subtracted by the p-value of Z when X = 99, hence:

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

By the Central Limit Theorem

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

[tex]Z = \frac{99 - 108}{4}[/tex]

[tex]Z = -2.25[/tex]

[tex]Z = -2.25[/tex] has a p-value of 0.0122.

1 - 0.0122 = 0.9878.

0.9878 = 98.78% probability that the mean lifetime of components in this sample will be longer than 99 months.

A similar problem is given at https://brainly.com/question/24663213


Related Questions

PLS HELP ASAP !!

A boy has climbed 210m up a 350m vertical cliff, and is trapped there.
A rescue helicopter is hovering 65m above the top of the cliff.
Calculate how far a rescue must be lowered to reach the boy.
You may draw a sketch to help you.

(i'll mark as brainliest if u answer:))

Answers

Answer:

205

Step-by-step explanation:

helicopter=65m

tap of the cliff=

the boy=350m

210=

that makes the answer 205

Answer:

205 meters

Step-by-step explanation:

The cliff is 350m, and the rescue helicopter is 65m above the top of the cliff.

This means that the helicopter is 415 meters above the bottom of the cliff.

The boy is 210m above the bottom of the cliff.

So, you have to subtract 210 from 415 to get 205.

Therefore, you have to lower the rescue 205m to reach the boy.

HELP IM LATE LOL In an aquarium, ⅖ of the fish are surgeonfish. Of these, ¾ are yellow tangs. What portion of all fish in the aquarium are yellow tangs?

Answers

Answer:

1 and 3/20 total, 15/20 of the fish are yellow tangs which would also be 75%.

Step-by-step explanation:

2/5 and 3/4 need to be converted into a fraction with a similar denominator. 5x4= 20, so 20 is our denominator.

To find the numerator, we need to multiply 2 by 4, which equals 8, and 3 by 5 which equals 15.

8/20 + 15/20 = 23/20 or 1 3/20

What is the missing numerator?


blank over seven minus three-eighths equals twenty-seven fifty sixths


4

5

6

7

Answers

Answer:

6

Step-by-step explanation:

6/7 - 3/8= 27/56

Answer:

it is 6

Step-by-step explanation:

3 (x-1)=3x-×-3-3+x+3
True or false

Answers

true

Step-by-step explanation:

Answer:

3x-3

Step-by-step explanation:

So false if you Multiply

20 points! :D

Not sure how to do this. :/

Answers

Answer:

t = (A - P) / Pr

Step-by-step explanation:

A = P + Prt

A - P = Prt

(A - P) / Pr = t

t = (A - P) / Pr

I need help asap please!

Answers

It’s asking if AED is congruent to ABC. The answer would be Yes. Triangle AED is congruent to triangle ABC.

Write the equation in point slope form

Answers

Answer:

5<6 so tbh I have no idea what this is I just need point

how do you do vectors

Answers

Answer:

i learn and solve them easily they r easy

A coat is priced $50. If the sales tax is 7% of the price, how much is the sales tax? What is the total cost including sales tax?

Answers

Answer:

The sales tax is $3.5

The total cost is $53.5

Step-by-step explanation:

To find the sales tax, you have to find the 7 percent of 50 dollars. In decimal form, 7% is 0.07. So you just have to multiply 0.07 to 50.

50 x 0.07 = 3.5

That's why $3.5 is the sales tax.

In order to get the total cost including sales tax. You just have to add $50 to the sales tax which is $3.5.

$50 + $3.5 = $53.5

Help me with this please

Answers

Answer:

5

Step-by-step explanation:

By process of elimination, we can say for sure that C and D are not the right answers because as x- the numbers on the top- increases, y- the numbers on the bottom- increases. This means that the slope is not negative, because the slope is the rate of change and it does not have a negative rate of change.

The equation for slope is y2-y1 / x2-x1. Meaning, y is on top and x is on bottom. This creates a fraction. So let's take 0 and 1 for X, the first and second values, and 3 and 8 for y, the first and second values. We swap them, because the second y value comes first, so we have 8 - 3 for the top, the numerator. Then we have 1 - 0 for the bottom, the denominator. Solving 8 - 3 and 1 - 0, we have 5/1. 5/1 simplifies to 5, and thus 5 is your slope.

find the proabilty of rolling factors of 5 on both sides.

Answers

I believe the answer is 1/5

, leisan can drive 32 miles on every gallon of gasoline. if she fills up her tank for $2.39 per gallon, how much will it cost her to drive 448 miles?

Answers

Answer:

It will cost her $33.46

Step-by-step explanation:

She drives 32miles per gallon

In 448miles, she will use: (448 × 1)/32

= 14gallons

If a gallon costs $2.39

Then 14gallons will cost, 14×2.39

= $33.46

steve has been lifting 225 pounds during a deadlift for several weeks. during his warmup he wants to lift 60% of this weight. how much weight should he lift?

Answers

Answer:

135 lb

Step-by-step explanation:

Turn 60% into a decimal (0.60)

Then multiply 225 by 0.60

225 * 0.60 = 135 lb

HOW MUCH IT’S ( 4/2 - 1/2 ) + 3/4 I need the answer because I’m stay in test

Answers

Answer:

= 7.25

Conversion a mixed number 4 3/

4

to a improper fraction: 4 3/4 = 4 3/

4

= 4 · 4 + 3/

4

= 16 + 3/

4

= 19/

4

To find a new numerator:

a) Multiply the whole number 4 by the denominator 4. Whole number 4 equally 4 * 4/

4

= 16/

4

b) Add the answer from previous step 16 to the numerator 3. New numerator is 16 + 3 = 19

c) Write a previous answer (new numerator 19) over the denominator 4.

Four and three quarters is nineteen quarters

Conversion a mixed number 2 1/

2

to a improper fraction: 2 1/2 = 2 1/

2

= 2 · 2 + 1/

2

= 4 + 1/

2

= 5/

2

To find a new numerator:

a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/

2

= 4/

2

b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5

c) Write a previous answer (new numerator 5) over the denominator 2.

Two and one half is five halfs

Add: 19/

4

+ 5/

2

= 19/

4

+ 5 · 2/

2 · 2

= 19/

4

+ 10/

4

= 19 + 10/

4

= 29/

4

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(4, 2) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 2 = 8. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - nineteen quarters plus five halfs = twenty-nine quarters.

Step-by-step explanation:

Answer:

you can write it in exact form which is 9/4 or decimal form which is 2.25 or mixed number form 2 1/4

Step-by-step explanation:

Help ASAP please i will mark brainliest who finishes first
pls be nice and neat
dont send links you CAN send photos of your answers
but i prefer typing your answers down thank you so much

Answers

Answer:

1-a) 78+x+16+x+24=180°

118+2x=180

2x=62

so x=31

Step-by-step explanation:

thats a

Answer:

1a) x = 31

1b) x = 12

2) angle A = 60 degrees

3) x = 40 degrees

Step-by-step explanation:

Rafael has two coupons for a phone.

Coupon A:

Coupon B:

$8 rebate on a $57 phone

20% off of a $57 phone

Choose the coupor that gives the lower price.

Then fill in the blank with the correct value.

Coupon A gives the lower price.

The price with coupon A is $] less than the price with coupon B.

Coupon B gives the lower price.

The price with coupon B is $] less than the price with coupon A.

lol

Answers

Coupon B would give the lower price because 20% off 57 is 45.60 and 8 dollars off 57 is 49

The length of a planet's orbit around a star is approximately 22,200,000 km. It takes the planet about 1230 Earth days to complete a full orbit. What is the planet's average speed in kmh-1 to 3sf?​

Answers

Answer:

Approximately [tex]12.9\; \rm km \cdot h^{-1}[/tex], assuming that this orbit is circular.

Step-by-step explanation:

The question is asking for a tangential velocity with the unit [tex]\rm km \cdot h^{-1}[/tex]. The unit of the given distance is already in [tex]\rm km[/tex] as required. Convert the unit of the orbital period to hours:

[tex]\begin{aligned}T &= 1230\; \text{day} \times \frac{24\; \rm h}{1\; \text{day}}. = 29520\; \rm h\end{aligned}[/tex].

Calculate the angular velocity [tex]\omega[/tex] of this planet from its orbital period:

[tex]\begin{aligned}\omega &= \frac{2\, \pi}{T} \\ &= \frac{2\, \pi}{29520\; \rm h} \approx 2.1285 \times 10^{-4}\; \rm h^{-1}\end{aligned}[/tex].

Given the radius [tex]r[/tex] of the orbit of this planet, the tangential velocity [tex]v_{\perp}[/tex] of this planet would be:

[tex]\begin{aligned}v_{\perp} &= \omega\, r \\ &\approx 2.1285 \times 10^{-4}\; \rm h^{-1} \times 2.22\times 10^{7}\; \rm km \\ &\approx 4.73 \times 10^{3}\; \rm km \cdot h^{-1}\end{aligned}[/tex].

If the orbit of this planet is circular, the velocity of the planet would be equal to its tangential velocity: [tex]4.73\times 10^{3}\; \rm km \cdot h^{-1}[/tex].

Antoin has 17.5 kilograms of clay. He divides it evenly into buckets that hold 2.5 kilograms. How many buckets of clay will he have?​

Answers

Answer:

7 buckets.

Step-by-step explanation:

17.5 / 2.5 = 7

Answer:

7

Step-by-step explanation:

17.5/2.5=7

a. 17 + 6 10=17,6 b. 45 + 6 100 5 c. 3 + + 10 2 100 7 8 d. 6 + + 9 + 10 100 1 000 6 e. 11 + + 10 8 1 000 f. 84 + 1 3 + 100 10
Need help me​

Answers

Step-by-step explanation:

a. 17 + 6/10 = (17 x 10) / (1 x 10) + 6/10 = 170/10 + 6/10 = 176/10 = 17,6

b. 45 + 6/100 = (45 x 100) / (1 x 100) + 6/100 = 4 500/100 + 6/100 = 4 506/100 = 45,06

c. 3 + 5/10 + 2/100

= (3 x 100) / (1 x 100) + (5 x 10) / (10 x 10) + 2/100

= 300/100 + 50/100 + 2/100

= 352/100 = 3,52

d. 6 + 7/10 + 8/100 + 9/1 000

= (6 x 1 000) / (1 x 1 000) + (7 x 100) / (10 x 100) + (8 x 10) / (100 x 10) + 9/1 000

= 6 000/1 000 + 700/1 000 + 80/1 000 + 9/1 000

= 6 789/1 000 = 6,789

e. 11 + 6/10 + 8/1 000

= (11 x 1 000) / (1 x 1 000) + (6 x 100) / (10 x 100) + 8/1 000

= 11 000/1 000 + 600/1 000 + 8/1 000

= 11 608/1 000 = 11,608

f. 84 + 1/100 + 3/10

= (84 x 100) / (1 x 100) + 1/100 + (3 x 10) / (10 x 10)

= 8 400/100 + 1/100 + 30/100

= 8 431/100 = 84,31.

Hope this helps!!

PLS ANSWER ASAPP!!

THX

Answers

TanA = 6/8
or 3/4 when simplified

Mario is a garbage collector in Mabuhay Homes 2000. He can collect garbages in 80 houses in just 5 working days. In 8 days straight work, he reached 140 houses.

Find the changes of Mario's work, in working straightly?

What was the total number of houses he collected in 12 days if he worked straight?

What will be total number of houses he can collect in 20 days if he will work straight continually?

Answers

192 because 80 divided by 5 equals 16 and 16 multiplied by 12 (12 working days) is equal to 192

Decide if the following situation is a unit rate or not why or why not?
You score 12 points in one basketball game.

Answers

Answer:

Yes, because in 1 game you scored 12 points you didn't score multiple points in multiple games.

please, help!!!! Bussines Calc. I give 20 points. I need a full explanation.

Answers

I believe you are trying to find the most Cheapest cost?

Since the area had to be 1200m^2 the most biggest numbers we could divide with is 30 x 40, which equals to 1200.

30 x 20 (expensive one the lower) = 600 (wall 3) + 20 x 20 = 1000 (wall 3 + wall 1)

40 x 13 (cheapter one the higher) = 520 (wall 4) + 32 x 13 = 936 (wall 4 + wall 2)

Add all together, $1936 to build the whole fence.

(I don't know for sure if I am right. If I am right, can I have a brainliest?)

here!i need the answer!
[tex]\sf 13\times 13\times 1[/tex]

Answers

Answer:

[tex]169[/tex]

Step-by-step explanation:

[tex]13 \times 13 \times 1[/tex]

[tex] = 13 \times 13[/tex]

[tex] = 169[/tex]

2x+7y=5
2x-7y=19
elimanation or substution

Answers

Answer:

(6, -1)

Step-by-step explanation:

4x = 24

x = 6

2(6) + 7y = 5

12 + 7y = 5

7y = -7

y = -1

Which point on the number line represents a loss of 5 yards in a football game? (number line is on picture)

A) Point A
B) Point B
C) Point C
D) Point D

please help me with this! it’s in need

Answers

The answer for this is b : point b because that represents -5

It takes 25 minutes to prepare the cake mixture and 70 minutes to bake in the
Kirsty is going to make a birthday cake for the party.
Kirsty then needs three quarters of an hour to decorate the cake.
The cake needs 1.5 hours to cool before decorating.
She wants to finish decorating the cake at least 2 hours before the
oven.
party starts.
The party starts at 2.30 pm.
What time should Kirsty start making the cake?
Show why you think this.

Answers

Answer:

she will start making it at 10 am

BRAINLIEST x 3
It is kinda late and I need to finish my work
Please help me
If you answer this I will create two other posts to give you extra brainliests

Answers

5. x=13
6. x=7
7. x=26
8. x=18
9. x=11 y=3
10. x=24
11. x=18 y=5
12. x= 17 y= 9

hope this helped!:)

I will give brainliest, assuming it allows me too

Answers

Answer: 611.64

Step-by-step explanation: add the check up and you get the total (answer)

Answer:

Step-by-step explanation:

it is sum of all amount of check values divided by no of those values  

sum / 5

What is the value of the expression 3q - 6 when q = -2?

Answers

Answer:

-12

Step-by-step explanation:

3q-6=x q=-2

(3(-2))-6

-6-6=x

-12=x

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