The lifetimes of a certain brand of light bulbs are known to be normally dsitributed with a mean of 1700 hours and standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. The probability is 0.20 that the sample mean lifetime is more than how many hours?
A. 1652.
B. 1725.
C. 1752.
D. 1670.

Answers

Answer 1

Answer:

1742 hours

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.

Single light:

Mean of 1700 hours and standard deviation of 400 hours, which means that [tex]\mu = 1700, \sigma = 400[/tex]

Sample of 64:

This means that [tex]n = 64, s = \frac{400}{\sqrt{64}} = 50[/tex]

The probability is 0.20 that the sample mean lifetime is more than how many hours?

This is the 100 - 20 = 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.84

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

By the Central Limit Theorem

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

[tex]0.84 = \frac{X - 1700}{50}[/tex]

[tex]X - 1700 = 50*0.84[/tex]

[tex]X = 1700 + 50*0.84[/tex]

[tex]X = 1742[/tex]


Related Questions

the last one is 3/20​

Answers

Answer:

the answer is C my man. I believe so

Answer:

I believe it is C.

Step-by-step explanation:

Write 10 3 without an exponent what number Is this ? 5.102+ 3

Answers

The value of 10^3 in standard form is 1000

Exponents and values

Give the exponential form 10^3

This means the product of 10 in 3 places. Mathematically;

10^3 = 10 * 10  10 * 10

10^3 = 100 * 10

10^3 = 1000

Hence the value of 10^3 in standard form is 1000

Learn more on standard form here: https://brainly.com/question/19169731

Steve completed 25% of the 40 math problems that were assigned for
homework. How many more problems does Steve need to complete?
Lindsaya

Answers

Answer:

30

Step-by-step explanation:

40-25%=30

Answer:

30

Step-by-step explanation:

quarter it, 25% of 40 is 1/4 so 30

Q.1 Thee are five girls and three boys in a group. The teacher chose one person at random. How could the teacher make a random choice?

Q.2 A random number generator generates a whole number in the range 1 to 100. What is the probability it is 40 or more if the number is greater than 25?

Answers

Answer:

Q1: She can write names of each Student on separate Papers and choose one Randomly, the Result may be 5:3 Girls to Boys

Q2: 75/100

If a person can see 6 miles from a height of 25 feet, how far can a person see from a height of 196 feet?

Answers

Answer:

24 miles

Step-by-step explanation:

A rectangular price tag has a cemeter of 30 centimeters, It's area is 54 square centimeters
What are the dimensions of the price tag

Answers

Answer:

l = 9 inches and b = 6 inches.

Step-by-step explanation:

Given that,

The perimeter of a rectangular price tag, P = 30 cm

The area of rectangular price tag, A = 54

We need to find the dimensions of the price tag.

The area of rectangle is given by :

A = lb

So,

54=lb ...(1)

The perimeter of a rectangle is given by :

P = 2(l+b)

So,

30=2(l+b)

15=(l+b) ...(2)

We need to solve equation (1) and (2) such that,

l = 9 inches and b = 6 inches.

What is 13x + 21y - 14x - y simplified?

Answers

Answer:

-x + 20y

Step-by-step explanation:

trust me.. its right

Help ASAP I’ll mark brainliest

Answers

D because negative is down right

Answer:

D

Step-by-step explanation:

It starts at the left and starting at the left the points start to go down which means it is negative

NEED ANSWER ASAP DUE TODAY!!!!!

Calculate the value of each expression.

a. (-8) times 2/3

b. (-8) times (-2/3)

c. -18/3

d. 18/-3

e. -18/-3

Answers

Answer:

a. -16/3

b. 16/3

c. -6

d. -6

e. 6
A b c d e are the answers

how do you subtract a deciamal with different denominators?​

Answers

Answer: decimals dont have denominators fractions do

Complete the statement to illustrate the commutative property. (PLEASE ANSWER FAST FOR BRAINLIEST!!!)
10 + (9 + 11) = 10 + (11 + ___ )

a. 11
b. 20
c. 9
d. 10

Answers

Answer:

9

--- your answer is 9 oof

9. The answer is C!!!!!!

This table shows how long, in minutes, it takes Jeremiah to run his miles.
How long does it take him to run 5 miles? *

Answers

Answer:

45

Step-by-step explanation:

follow the table of 9.

9x2=18

9x3=27

9x4=36

9x5=45

Find the measure of x, then the measure of А
(33-9x)"
48/Dc
x =
degrees


I need it now please!!!

Answers

Answer:

x = - 11 ; m∠B = 132°

Step-by-step explanation:

(33 - 9x)° + 48° = 180°

33 - 9x + 48 = 180

81 - 9x = 180

- 9x = 99

x = - 11

m∠B = [33 - 9(- 11)]° = (33 + 99)° = 132°

m∠B = 132°

Simplify the following expression
4[7+2/3-2(3/5)]

Answers

Answer:  Add 7+ [tex]\frac{2}{3}= \frac{7}{1} + \frac{2}{3} = \frac{7.3}{1.3} + \frac{2}{3} = \frac{21.2}{3} = \frac{23}{3}[/tex] 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 the both denominators - LCM(1, 3) = 3. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 3 = 3. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - seven plus two thirds = twenty-three thirds.

Multiple: 2 * [tex]\frac{3}{5} = \frac{2.3}{1.5} = \frac{6}{5}[/tex] Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(6, 5) = 1. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - two multiplied by three fifths = six fifths.

Subtract = [tex]\frac{23}{3} - \frac{6}{5} = \frac{23.5}{3.5} - \frac{6.3}{5.3} = \frac{115}{15} - \frac{18}{15} =\frac{115 - 18}{15}[/tex]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 the both denominators - LCM(3, 5) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 5 = 15. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - twenty-three thirds minus six fifths = ninety-seven fifteenths.

Multiple: 4 Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(388, 15) = 1. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - four multiplied by ninety-seven fifteenths = three hundred eighty-eight fifteenths.

Step-by-step explanation:

hope this helps

Extend the pattern below by four terms write an observation about the pattern pattern 76, 70, 64,58,52

Answers

Answer:

46, 30, 24, 18, 12

Step-by-step explanation:

(3b+2)(b-8) multiply

Answers

Answer:

3b^2-22b-16

Step-by-step explanation:

3b^2-24b+2b-16=

3b^2-22b-16

Answer:

3b^2 -22b -16

Step-by-step explanation:

(3b+2)(b-8)

FOIL

first :3b*b = 3b^2

outer : 3b *-8 = -24b

inner: 2*b = 2b

last: 2*-8 = -16

Add them together

3b^2 -24b+2b -16

Combine like terms

3b^2 -22b -16

Fourteen increased by 6 times a number is 32?

Answers

14 times 6 is 84, sorry if I didn’t understand your question
14+6*3= 32 your missing number would be 3. I’m 100% Sure.

What is the average rate of change of the function g(x) = 4x from x = 1 to x = 5?

Answers

Answer:

[tex]\displaystyle 4[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

Function NotationInterval Notation - [a, b]Average Rate of Change: [tex]\displaystyle \displaystyle \frac{f(b) - f(a)}{b - a}[/tex]

Step-by-step explanation:

Step 1: Define

g(x) = 4x

Interval [1, 5]

Step 2: Find Change

Substitute in function and points [Average Rate of Change]:                     [tex]\displaystyle \displaystyle \frac{4(5) - 4(1)}{5 - 1}[/tex][Fraction] Multiply:                                                                                          [tex]\displaystyle \displaystyle \frac{20 - 4}{5 - 1}[/tex][Fraction] Subtract:                                                                                         [tex]\displaystyle \displaystyle \frac{16}{4}[/tex][Fraction] Divide:                                                                                              [tex]\displaystyle 4[/tex]

What is the equation of the line that is parallel to y = 3x - 1 and goes through the point (0, 9)?

Answers

Answer:

Step-by-step explanation:

y - 9 = 3(x - 0)

y - 9 = 3x - 0

y = 3x + 9

A person places $85800 in an investment account earning an annual rate of 8.5%,

compounded continuously. Using the formula V = Pert, where V is the value of the

account int years, P is the principal initially invested, e is the base of a natural

logarithm, and r is the rate of interest, determine the amount of money, to the nearest

cent, in the account after 9 years.

Answers

Answer:

$184383.7

Step-by-step explanation:

We are given that

Principal, P=$85800

Rate of interest, r=8.5%=0.085

Time, t=9 years

We have to find the amount of money after 9 years

[tex]V=Pe^{rt}[/tex]

Using the formula

[tex]V=85800e^{0.085\times 9}[/tex]

[tex]V=184383.7[/tex]

Hence, the amount of money after 9 years=$184383.7


Expand and simplify 2(x + 7) + 3(x + 1)

Answers

Answer:

[tex]5x+17[/tex]

Step-by-step explanation:

We will have to expand first then we simplify.

Expand

You will have to distribute the 2 over the x & 7 and the 3 over the x & 1 respectively.

[tex]2(x+7)+3(x+1)=2x+14+3x+3[/tex]

Simplify

You will have to add 2x & 3x together and 14 & 3 together.

[tex]2x+14+3x+3=5x+17[/tex]

Answer

[tex]5x+17[/tex]

Puzzles are packaged in groups of 3. If the store has 183 nature puzzles and 165 animal puzzles, how many packages of puzzles are there?

Answers

Answer: 116 packages

Step-by-step explanation:

From the question, we are informed that Puzzles are packaged in groups of 3 and that the store has 183 nature puzzles. The number of packages here will be:

= 183/3

= 61 packages

For the 165 animal puzzles, the number of packages will be:

= 165/3

= 55 packages

The total number of packages of puzzles will be:

= 61 + 55 packages

= 116 packages

Answer:

116

Step-by-step explanation:

First find total number of puzzles.

183+165=348

Then divide the total puzzles by puzzles in a package (3)

348÷3=

116 packages of puzzles

Check all the statements that are true:

a. A predicate is a proposition-valued function.
b. It is possible to define disjunction using only negations and conjunction.
c. A conditional is false when both premise and conclusion are false.
d. Domain-restricted universal quantification is logically equivalent to the unrestricted universal quantification of a conditional.
e. The negation of a conjunction is the disjunction of the negations.
f. Inverse and converse are logically equivalent.
g. (p→q)∧(p→¬q) is a contradiction.
h. (p→q)∨(p→¬q) is a tautology.
i. Domain-restricted existential quantification is logically equivalent to the unrestricted existential quantification of a conditional.
j. The contrapositive is the inverse of the converse.

Answers

Answer:

a. True

b. False

c. True

d. True

e. False

f. True

g. False

h. True

i. True

j. True

Step-by-step explanation:

The statement a and i are true. The predicates can be defined without an input variable. These numerical variables can be defined without an input variable. The statement b is false since the p to q is not in conjunction rather its contradiction.

Answer:

true

false

true

true

false

true

false

true

true

true

A total of 328 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the
number of adult tickets sold. How many adult tickets were sold?

Answers

Answer:

246 adult tickets were sold

Step-by-step explanation:

System of equations:

Variables:

x = number of adult tickets sold

y = number of student tickets sold

There were a total of 328 tickets sold, thus:

x + y = 328

The number of student tickets sold was three times the number of adult tickets sold, thus:

y = 3x

Substituting in the first equation:

x + 3x = 328

Simplifying:

4x = 328

Dividing by 4:

x = 328/4

x = 82

y = 3*82= 246

246 adult tickets were sold

It is not suppose to say college. (not part of the question)

Encountering a head wind of 30 miles per hour, it took a plane, whose speed would have been 450 miles per hour, 6 hours to fly from San Diego to Honolulu. What was the distance between these two points?

Answers

Answer:

32 I would say is the correct answer to this question

Can somebody please help me!!

Answers

Answer:

C≈15.71

Step-by-step explanation: use the circumference formula

Answer:
C≈15.71
Explanation:
Simply, use the circumference formula in order to find the circumference of the circle and then round it to the nearest hundredth.

PLEASE helppp I will give brainsssss!! FInd x and y

Answers

Answer:

x = 10°, y = 20°

Step-by-step explanation:

Fill in the missing angle measures, 20° and 70°.

7x = 180 - 90 - 20

7x = 70

x = 10

2y = 180 - 7x - 5x - 20 = 40

y = 20

X=10
Y=20

Explanation-you would take 20+90 then subtract that from 180 which gives you 70 and 7x10 is equal to 70. 70+110=180. If x=10 then 5x would give you 50, then you add 20 and get 70. Then you add another 70 because the angle between the green line and black line is equal to 7x. This would give you 140. So 2y would have to be 2(20) which give you the remaining 40.

Two chemical plants, one at Macon and one at Jonestown, produce two types of fertilizer, low phosphorus (LP) and high phosphorus (HP). At each plant, the fertilizer is produced in a single production run, so the two types are produced in fixed proportions. The Macon plant produces 1 ton of LP and 3 tons of HP in a single operation, and it charges $600 for what is produced in one operation, whereas one operation of the Jonestown plant produces 1 ton of LP and 1 ton of HP, and it charges $1,000 for what it produces in one operation. If a customer needs at least 100 tons of LP and 180 tons of HP, how many production runs from each plant should be ordered to minimize the cost.

Answers

9514 1404 393

Answer:

  100 runs from Macon

Step-by-step explanation:

A graph of the requirements shows the feasible region is bounded by a polygon with vertices (Macon, Jonestown) = (0, 180), (40, 60), and (100, 0).

Checking costs of these solutions, we find the lowest cost to be obtained when ...

  100 production runs should be ordered from Macon

Vishal's phone plan costs $45.37 per month plus $0.60 per text message. How many text messages can he send and keep his monthly costs to no more than $79?

Answers

The answer is 56 text messages



Cost of materials used $45,000

Direct labor costs 48,000

Factory overhead 39,000

Work in process, beginning 18,000

Work in process, ending 28,000





What is the cost of goods manufactured?

a.
$122,000
b.
$132,000
c.
$142,000
d.
$178,000

Answers

d $178,000 cost of foods

Other Questions
What was the average day for women in the 1940s?Give at least three responses The 1980's saw a handful of revolutionary attempts either towards communism or awayfrom it that the Reagan Administration tried to interfere with in which which region ofthe world? The statement "one-eighth the age, a" can be expressed algebraically as ? what does GCAT help us remember? What ate all of the x-intercepts of the continuous function in the table? 9(2,-3)-5(+8)FAST LOLOLOL Your friend shows you a coin collection. In it, 45/50 of the coins are quarters. What percent of the coins are quarters? THIS IS THE LAST QUESTION PLEASE HELP!! TYSMMMMMMMM Which two claims are supported by the information in History by Ralph Waldo Emerson? Jesse bought 5.2 kilograms of grapes for AED 7.75. How much would 1 kilogram of grapes cos Which graphs cannot represent a proportional relationship? Explain how you know.PLEASE HELP THIS IS DUE AT 11pm Given the equity portion of a firm's balance sheets below, determine the average price per share at which new shares were sold by the firm in 2019. 2018 2019 Common Stock ($0.40 par) $620,600 $830,200 Capital Surplus $9,025,000 $13,726,000 Retained Earnings $17,400,000 $19,100,600 No answer text provided. $12.22 per share $9.37 per share $12.62 per share $8.97 per share Suppose that at the current price of a good, the quantity demanded is 44 units and the quantity supplied is 40 units. We can expect: Group of answer choices the price of the good to increase. the price of the good to decrease. the demand for the good to increase. the supply of the good to decrease. with one ? 1. Basketball is his ... passion.a. consumption b. consurning c. consumerof patterns to choose from.d. consumerism ?El inspector de aduana pregunta, ia tiene algo para declarar b.cuntos aos tieneC.le gusta la pelculaPlease select the best answer from the choices provided The figure shows different possible transitions of electrons as they move from higher energy states to lower energy states. Which transition will produce the spectrum line with the lowest wavelength in this elements atomic spectrum?A. AB. BC. CD. D The chart below shows data from butterfly populations over a four-year period. Use the data in the chart to answer the question that follows. Butterfly ColorYear 1Year 2Year 3Year 4Year 5Red100107180192?Blue1021083310?White120118175188?Yellow1101073917?Which of the following statements is a valid conclusion based on the data table above? A. In year 5, the red population will decrease because a change in the habitat occurred in year three that favored red butterflies. B. In year 5, the blue population will decrease because a change in the habitat occurred in year three that favored blue butterflies. C. In year 5, the red population will increase because a change in the habitat occurred in year three that favored red butterflies. D. In year 5, the blue population will increase because a change in the habitat occurred in year three that favored blue butterflies. When 5.0g of NH4CLO4 is added to 100mL of water in a calorimeter, the temperature of the solution formed decreases by 3.0C? Find the determinant of the matrix. Expand by cofactors on the row or column that appears to make the computations easiest. Solve the Antiderivative