A Government company claims that an average light bulb lasts 270 days. A researcher randomly selects 18 bulbs for testing. The sampled bulbs last an average of 260 days, with a standard deviation of 90 days. If the CEO's claim were true, what is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days

Answers

Answer 1

Answer:

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 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 [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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question, we have that:

[tex]\mu = 270, \sigma = 90, n = 18, s = \frac{90}{\sqrt{18}} = 21.2[/tex]

What is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days?

This is the pvalue of Z when [tex]X = 260[/tex]. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{260 - 270}{21.2}[/tex]

[tex]Z = -0.47[/tex]

[tex]Z = -0.47[/tex] has a pvalue of 0.3192.

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days


Related Questions

A taxi company charges $9 for pick-up plus $0.35 for each mile. Select the expressions that represent the cost in dollars for a taxi pick up and m miles. Select all that apply.

A. 9+0.35m
B. 9m+ 0.35
C. 0.35m+9
D. The product of 9 and m plus 0.35

Please answer quick

Answers

Your answer is A and C

If 45% of a number, n, is 225, what is 74% of n?

Answers

Answer: 375

hope this helps :D

Step-by-step explanation:

225/45=5

5=1%

5 times 74 equals 375

△GFH is similar to △CDE. Identify the corresponding congruent angles.

Answers

Answer:

∠G ≅  ∠C

∠F ≅  ∠D

∠H ≅  ∠E

Step-by-step explanation:

if you have 4 B's and 2 A's then what is your GPA

Answers

Answer:

3.33

Step-by-step explanation:


(4a^15b)^3 there is a photo to go with it

Answers

Answer:

I believe it's option 3

explanation: you times inside by 3

Answer:

option 1.

Step-by-step explanation:

(4a⁵b)³ = 4³ * (a⁵)³ * b³

           [tex]= 64 *a^{5*3} * b^{3}\\\\= 64a^{15}b^{3}[/tex]

PLEASE HELP, QUICK

10 POINTS

Answers

Answer:

x = 1

y = 10

(1,10)

hope that helps :)

Write the equation of the line in point-slope form that goes through the points (0, 1) and (2, 7)

Answers

Answer:

point - slope form

 y - 1 = 3 (x-0)

Step-by-step explanation:

step(i):-

Given points are (0,1) and (2,7)

The slope of the line

     [tex]m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

    [tex]m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } = \frac{7-1}{2-0} = \frac{6}{2} = 3[/tex]

  m =3

Step(ii):-

point -slope form

   y - y₁ = m(x-x₁)

Equation of the straight line passing through the point (0,1) and having slope 'm' = 3

   y - 1 = 3 (x-0)

  y -1 = 3x

 3x - y +1=0

Equation of the straight line passing through the point (0,1) and having slope 'm' = 3 is 3x -y +1=0

Solve for X
X/3-X/4=X/6

Answers

[tex] \huge \blue{solution}[/tex]

[tex] \bold \red{ \frac{x}{3} - \frac{x}{4} = \frac{x}{6} }[/tex]

[tex] \bold \red{ \frac{4x + 3( - x)}{3 {2}^{2} } = \frac{x}{6} }[/tex]

[tex] \bold \red{ \frac{4x - 3x}{3 {2}^{2} } = \frac{x}{6} }[/tex]

[tex] \bold \red{\frac{x}{3 {2}^{2} } = \frac{x}{6} }[/tex]

[tex] \bold \red{ - x = 0}[/tex]

[tex] \bold \red{x = 0}[/tex]

w+6=2(w-6) what is the answer?​

Answers

Answer:

w = 18

Step-by-step explanation:

w+6 = 2(w-6)

w+6 = 2w-12

2w-w = 6+12

w = 18

hope it helps

Answer:

[tex] \huge \boxed {w = 18}[/tex]

Step-by-step explanation:

Distribute 2 in the bracket.

[tex]w + 6 = 2w - 12[/tex]

A constant and variable cannot add up or subtract each others. Therefore, move the same term to the same side.

[tex]12 + 6 = 2w - w \\ 18 = w[/tex]

Answer Check

Substitute w = 18 in the equation.

[tex]18 + 6 = 2(18) - 12 \\ 24 = 36 - 12 \\ 24 = 24[/tex]

Therefore w = 18 is the correct answer.

PLEASE HELP MEEE ASAP THIS IS DUR SOON

Answers

Answer:

I am pretty sure it is A because it is -5 and then +2

Step-by-step explanation:

I hope this is right

I hope this helps you...

Answer:

option A

Step-by-step explanation:

the arrow goes from 0-5 then another from 5-3

12. What is the value of the y-coordinate of the solution to the system of equations x - 2y = 1 and x + 4y = 7?
(1) 1
(2) -1
(3) 3
(4) 4​

Answers

Answer:

(3,1)

value x is 3

value y is 1

What is the slope of the line below?

Answers

Answer:

37

Step-by-step explanation:

I saw it there in the picture

Answer:

m=2

Step-by-step explanation:

use the slope formula m=y2-y1/x2-x1

Points: (0,4) (-2,0)

m=0-4/ -2-0

m=-4/-2

m=2

I really need help on this please and thank you in advance

Answers

Answer:

Step-by-step explanation:

first, your answer will be negative,

x^12*(2y)^3=x^12(8y^3)

denominator= -x^2*y^12

after we divide them=- 8 x^10/y^9

choice E

10.
(02.01 LC)
Simplify 8 over negative 4 ÷ negative 3 over 9 . (5 points)

6
-6
12
-12

Answers

Answer:

The answer is 6

Step-by-step explanation:

First nothing us negative, so multiply 8/4 times 9/3,which is 72/12=6, 6×12 is 72.The reason why it is 9/3 instead of 3/9 is because you are dividing so KCF, keep change flip.

Answer:

Positive 6

Step-by-step explanation:

What you do is:

8 x 9 = 72

-4 x (-3) = 12

72 / 12 = 6

Hope this helps!

- 28allemm

What is 150% of 625? Solve using an equation.

Answers

Answer:

937.5

Step-by-step explanation:

150%=150/100

Equation:150/100 x 625

937.5

2. in a class of 50 students, the number of females is 2 more than 5 times the number of males. How many males and females are there in the class?

Answers

Answer:

There are 8 males in the class and 42 females.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the number of females.

y is the number of males.

Class of 50 students

This means that [tex]x + y = 50[/tex]

The number of females is 2 more than 5 times the number of males.

This means that [tex]x = 5y + 2[/tex]

So, finding y, the number of males:

[tex]x + y = 50[/tex]

[tex]5y + 2 + y = 50[/tex]

[tex]6y = 48[/tex]

[tex]y = \frac{48}{6}[/tex]

[tex]y = 8[/tex]

Females:

[tex]x = 5y + 2 = 5*8 + 2 = 42[/tex]

There are 8 males in the class and 42 females.

Please help me answer this

Answers

Answer:

Brand A

Step-by-step explanation: Brand A because y=50x+100 and that equals 150x. For brand B y=25x+200 and that equals 225x. So Brand A is lower.

You and your family went out to eat at The Cheesecake Factory. The bill is $120, you want to leave an 18% tip and have to pay a 6% tax. What is the total you have to pay for the everything?

Answers

Find the tip:

$120 * 18% =

$120 * 0.18 =

$21.60

Find the tax:

$120 * 6% =

$120 * 0.06 =

$7.20

Find the answer:

$120 + $21.60 + $7.20 =

$148.80

2) You traveled 210 miles in 3.5 hours.
How many miles will you travel per hour?

Answers

Answer:

= 56.7 miles per hour

Step-by-step explanation:

Step-by-step explanation:

To find the average speed for the entire journey, we need to find the entire distance   and the  total time

Entire distance = 210 miles + 130 miles = 340 miles

Total time = 3.5 hours and 2.5 hours = 6 hours

Average speed = distance/ time = 340 miles/ 6 hours

                           = 56.66666666666 miles per hour

Rounding to the nearest tenth

                             = 56.7 miles per hour

Answer:

60 miles

Step-by-step explanation:

Step 1:

210=3.5

x =1

Step 2: cross multiply

3.5×x= 210×1

3.5x=210

Step 3: divide both sides by the coefficient of x which is 3.5

3.5x/3.5=210/3.5

x=60

Answer= 60 miles

Bob drove 65 miles per hour for 3 hours, how far did he drive​

Answers

Answer:

195 miles

Step-by-step explanation:

Answer:

195 miles.

Step-by-step explanation:

In 1 hour Bob drove = 65 miles

In 3 hours, Bob drove = 3 * 65 = 195 miles.

Hope it will help :)

Solve: –3x – 7 < 11
Α) α
X > -2
B
2 <
2
С
x < -2
D
2 > -6

Answers

Answer:

Step-by-step explanation:

Here you go mate

Step 1

-3x-7<11  Equation/Question

Step 2

-3x-7<11  Simplify

-3x-7<11

Step 3

-3x-7<11  Add

-3x<18

Step 4

-3x<18  Divide by 3

answer

x>-6

Hope this helps

What is the slope of the line through (-4, 2) and (3,-3)?
Choose 1 answer:
A: -5/7
B: 7/5
C: 5/7
D: -7/5

Answers

Answer:

A

Step-by-step explanation:

To the nearest unit, what is the perimeter of this pentagon?
5
3
2
1
2
4
-6 -5 -4 -3 -2 -1 0
-1
2
-3
-4
-5
sh
27 units
0 29 units
0 30 units
0 34 units

Answers

Answer: 27 units

Step-by-step explanation: I just did the test and Got it right

A school supply company is giving away free whiteboards to promote their stain-free markers. The company can spend up to $42,840 on the whiteboards. If each whiteboard costs the company $8, how many whiteboards will they be able to give away?

Answers

Answer:the whiteboards free

Step-by-step explanation:

5,355 if you divide by 8

PLS HELP ASAP WILL GIVE BRAINLIEST

Answers

Answer:

it would be the second answer

Step-by-step explanation:

Answer:
It would be B

Easy math Can someone please help me

Answers

Answer:

4.2 cm

Step-by-step explanation:

Given

Area of parallelogram (A) = 4.2 cm²

base (b) = 1.75 cm

Height (h) = ?

We know

A = b * h

4.2 = 1.75 * h

h = 4.2 / 1.75

H = 2.4 cm

Hope it will help

.
If the cells continue to double every 5 minutes, how
long will it take to fill 3 additional bottles of the same
Size?
I minutes
Done
Intro

Answers

Answer:

10 min.

Step-by-step explanation:

Taylor will order one t-shirt for each person who attends her family's reunion. The cost is
$8 per t-shirt plus a one-time printing fee of $40.00. This can be represented by the
equation c = 8n + 40, where c represents the total cost of the shirts and n represents
the number of shirts ordered. If the family can spend no more than $600.00 on t-shirts,
what is the maximum number they can order?
B) 75
C) 70
A) 80
D) 15

Answers

Answer:

C) 70

Step-by-step explanation:

Since they can only spend a maximum of $600, we can fill that in for c. Now, we can solve the equation for n.

600 = 8n + 40

~Subtract 40 to both sides

560 = 8n

~Divide 8 to both sides

70 = n

Best of Luck!

1 foot = 12 inches therefore 5 feet = what

Answers

Answer:

60 inches

Step-by-step explanation:

1 foot = 12 inches

5 feet = ?

5*12 = 60

[tex]1\cdot \text{foot} = 12\cdot \text{inches} \implies 5 \cdot\text{foot} =5\cdot 12 \cdot\text{inches} \implies 5 \cdot\text{foot} =60 \cdot\text{inches}[/tex]

5 divided by 4 in fractions one with a whole and one without
Plsss help I don’t want an f

Answers

Answer:

5/4 or 1 1/4

Step-by-step explanation:

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