An elevator has a placard stating that the maximum capacity is 1580 lb-10 passengers.​ So, 10 adult male passengers can have a mean weight of up to 1580/10 = 158 pounds. If the elevator is loaded with 10 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 158 lb.​ (Assume that weights of males are normally distributed with a mean of 160 lb and a standard deviation of ​35 lb.) Does this elevator appear to be​ safe?

Answers

Answer 1

Answer:

a) 0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb

b) No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.

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 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.

Assume that weights of males are normally distributed with a mean of 160 lb and a standard deviation of ​35 lb.

This means that [tex]\mu = 160, \sigma = 35[/tex]

Sample of 10:

This means that [tex]n = 10, s = \frac{35}{\sqrt{10}} = 11.07[/tex]

a) Find the probability that it is overloaded because they have a mean weight greater than 158 lb.​

This is 1 subtracted by the pvalue of Z when X = 158. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{158 - 160}{11.07}[/tex]

[tex]Z = -0.18[/tex]

[tex]Z = -0.18[/tex] has a pvalue of 0.4286

1 - 0.4286 = 0.5714

0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb.

b.) Does this elevator appear to be​ safe?

No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.


Related Questions

WILL MARK B!
Please I need help I have a quiz

Answers

Answer:

a) 2x² - x + 3 = x(2x + 1) - 2x

<=> 2x² - x + 3 = 2x² + x - 2x

<=> 3 - x = - x

<=> 3 = 0

=> no solution

b) x/2 - x/3 - x/4 = 1/12

[tex] \frac{6x}{12} - \frac{4x}{12} - \frac{3x}{12} = \frac{1}{12} \\ \\ \frac{ - x}{12} = \frac{1}{12} \\ \\ = > - x = 1 \\ \\ \\ < = > x = 1[/tex]

=> the euqation has the solution x = 1

c) |x - 5| = 2|x|

=> x - 5 = 2x

or x - 5 = -2x

<=> x = -5

or 3x = 5

<=> x = -5

x = -5or x = 5/3

d) defined conditions: 2 - x 》 0

<=> x 《 2

we have:

[tex] \sqrt{x + 4} = 2 - x \\ < = > x + 4 = (2 - x) {}^{2} \\ < = > x + 4 = {x}^{2} - 4x + 4 \\ < = > {x}^{2} - 5x = 0 \\ < = > x(x - 5) = 0 \\ [/tex]

<=> x = 0 (because x 《 2)

e)

[tex] \sqrt{5} = \frac{1}{25 {}^{x} } \\ = > 5 = \frac{1}{25 {}^{2x} } \\ < = > 5.25 {}^{2x} = 1 \\ < = > 5.5 {}^{4x} = 1 \\ < = > 5 {}^{4x + 1} = 1 \\ = > 4x + 1 = 0[/tex]

<=> x = -1/4

Answer:

[tex]a) [x: - \infty < x < \infty ][/tex]

[tex]b)[x: - 1][/tex]

[tex]c) [x:- \frac{5}{3} ][/tex]

[tex]d) [x: 3, 0][/tex]

[tex]e) [x: - \frac{1}{4} ][/tex]

Suppose that 20% of voters are in favor of a certain legislation. A large number n of voters are polled and a relative frequency estimate fA(n) for the above proportion is estimated. How many voters should be polled so that the probability is at least 0.95 that fA(n) differs from 0.20 by less than 0.02?

Answers

Answer:

8000 voters

Step-by-step explanation:

E is the difference between probability that is real and those which are estimated

Sd² = p(1-p)

When solve this, using the formula in the attachment,

0.95 = 1-0.2(0.2)²/n(0.02)

0.95 = 1 - 0.16/n(0.02)²

1-0.95 = 0.16/n(0.02)²

0.05 = 0.16/0.0004n

We cross multiply here

0.05 x 0.0004n = 0.16

0.00002n = 0.16

Divide through by 0.00002 to get n

n = 8000

This is the number of voters that should be polled

The probability distribution for a
random variable x is given in the table.
-10
-5
0
5
10
15
20
Probability
.20
.15
.05
.1
.25
.1
.15
Find the probability that x = -10

Answers

Answer:

.20

Step-by-step explanation:

According to what are written in the table the probability for x=-10 is .20

The probability distribution  at x= -10 is 0.20.

What is Probability distribution?

A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.

Given:

We have table as,

x                  -10    -5      0      5      10    15     20

Probability 0.20 0.15 0.05 0.10 0.25 0.10 0.15

So , we have to find probability that x = -10 then by looking at table the corresponding value to x= -10 the probability is 0.20.

Learn more about Probability distribution here:

https://brainly.com/question/14210034

#SPJ2

First one to answer gets BRAINLIEST no cap look at the picture.

Answers

Answer:460

Step-by-step explanation:

A number greater than or equal to 41.

Answers

Answer:

42

Step-by-step explanation:

¯\_(ツ)_/¯

What is the midpoint of the segment below? (-12, -3) (3, -8)

Answers

Your answer is: D.

(-9/2,-11/2) use the midpoint formula

Which equation represents "The sum of a number n and 8, subtracted from 20, is 16."
A. n + 8-20 = 16
B. 8n - 20 = 16
C. 20 - (n + 8) = 16
D. 20- 8n = 16​

Answers

answers is A
B & D show n and 8 being multiplied and it says sum
if n=28 then that makes -16=16 on C and that is incorrect
when you plug in 28 for n on A it is 16=16

HELP PLS MIGHT GIVE BRAINLIST BUT ONLY IF 2 PEOPLE ANSWER!

Answers

Answer:

area of rectangle =72in

area of triangle = 3in

square in of plastic in ruler =69in

Please Help!!!!! Ill give thanks and rate best!

Answers

Answer:

1/216

1/8 *1/3³ ( cross multiply ) = 1/216

Did you only need the answer for the one on the top right?? Or all of them because If you need all of them I can do that too I am just assuming you just needed that one because it was selected.

HELP ME PLS ITS URGENT .. !❗❗❗❗❗❗❗❗❗❗❗❗❗
The commuting distances, in miles, of 10 employees were used to make the box plot shown above. Which of the sets of distances below matches the given box plot?
A.
Commuting Distances: 10, 15, 15, 20, 20, 20, 30, 30, 45, 45

B.
Commuting Distances: 10, 15, 15, 20, 20, 30, 30, 30, 45, 45

C.
Commuting Distances: 10, 15, 20, 20, 20, 20, 30, 30, 45, 45

D.
Commuting Distances: 10, 15, 15, 20, 20, 20, 30, 45, 45, 45

Answers

Answer:

A the answer is A ^w^ hope this helps

Could someone help me with with 6-10??

Answers

Answer:

You need a protractor

Step-by-step explanation:

to measure the angles

Pls help if not that’s fine just pls stop with the links

Answers

Answer:

C. 73 and 73

Step-by-step explanation:

An isosceles triangle has two angles that are the same, that narrows it down to C and D. The question states that there is only one 34° angle so it has to be C.

Answer:

C. 73° and 73°

Step-by-step explanation:

We know that the sum of interior angles in a triangle is equal to 180° and

Isosceles triangles has two angles with same measurement

it stated in the question that exactly one angle has measure of 34°

So the other two angles must be equal for the triangle to be isosceles

180 - 34 = 146 and this divided by 2

73° and 73° is the answer.

What is the COEFFICIENT in the expression s + 16?

Answers

8 I think I hope you get this right

Answer:

I think its 16

Step-by-step explanation:

What is the lateral surface area of this net



Help!!!

Answers

9514 1404 393

Answer:

  720 square feet

Step-by-step explanation:

The lateral area is the area of the central rectangle of the net. It is 12+12+12 = 36 feet long and 20 ft wide.

The lateral area is (36 ft)(20 ft) = 720 ft².

8. Determine the area of a sector
with a central angle of 42° in a
circle with radius 3 inches.

NEED IT ASAP

Answers

Answer:

[tex]\boxed {\boxed {\sf A \approx 3.3 \ in^2}}[/tex]

Step-by-step explanation:

Since we are given the central angle in degrees, we should use the following formula for sector area.

[tex]A= \frac {\theta}{360}* \pi r^2[/tex]

The angle is 42 degrees and the radius is 3 inches. Therefore,

[tex]\theta= 42 \\r=3 \ in[/tex]

[tex]A=\frac {42}{360} * \pi (3 \ in)^2[/tex]

Solve the exponent.

(3 in)²= 3 in*3in = 9 in²

[tex]A=\frac {42}{360} * \pi (9 \ in^2)[/tex]

Multiply all three numbers together.

[tex]A= 0.116666666667* 3.14159265359 * 9 \ in^2[/tex]

[tex]A=3.29867228627 \ in^2[/tex]

Let's round to the tenth place. The 9 in the hundredth place tells us to round the 2 up to a 3.

[tex]A \approx 3.3 \ in^2[/tex]

The area of the sector is approximately 3.3 square inches.

Please help!!!!!!!!!!!!!!!!!!!!!!

Answers

the right answer is B.

If k=9 and x=5, find the value of the expression:
2k - X

Please hurry

Answers

Answer:

[tex]\huge\boxed{13}[/tex]

Step-by-step explanation:

= 2k - x

Given that k = 9, x = 5

= 2(9) - 5

= 18 - 5

= 13

[tex]\rule[225]{225}{2}[/tex]

Hope his helped!

~AH1807

One interior angle of a triangle is 60⁰. The other angle measures are x⁰ and y⁰. Which of the following could be the values of x and y? Select all that apply. A. x = 50, y = 90 B. x = 45, y = 45 C. x = 40, y = 80 D. x = 100, y = 20 E. x = 60, y = 60

Answers

Answer:

B,C,D

Step-by-step explanation:

1, 3, 5, 7, 9, 9, 11, 11, 13, 14 }

Which box plot represents the data set?

Answers

It should be the second one

I need help finding the area and perimeter to this question. Pls help!! Thank you!

Answers

Answer:

Perimeter: 50.27

Area: 201.06

Step-by-step explanation:

The perimeter (circumference) is radius times pi times 2

This would be 8 times pi tomes 2 and when you do that you get 50.27

For the area you would do radius squared times pi

This would be 8 squared times pi which is 201.06

Hope this is helpful

- Please mark brainliest :)

Which expressions are equivalent to 5x-15? Select three options.
5(X+15)
5(x-3)
4x+3y-15-3y+X
-7y-6x-8y + x
0-20-3x+5+ 8x

Answers

Answer:

The number 2 for sure but i dont know the rest

Step-by-step explanation:

Round 7.54 please I need help

Answers

Round it to make it a whole number makes it 8 but in decimal form it would stay 7.5

A particular fruit's weights are normally distributed, with a mean of 372 grams and a standard deviation of 26 grams. If you pick 36 fruit at random, what is the probability that their mean weight will be between 365 grams and 380 grams

Answers

Answer: 90.93%

Step-by-step explanation:

M= 372

s= 26

n=36

P(365<x<380)

1. Find Z ----> 365-372 [tex]\sqrt{36}[/tex] = -1.6     Next Z---->  380 - 372 [tex]\sqrt{36}[/tex]=  1.8

                           26                                               26

2.  plug into calculator to find probablity: normalcdf(-1.6 , 1.8 ) = .90927 or 90.93% that the prob is between 365 and 380

Mrs Sogiba is catering for her son's birthday party. She has invited some of
her son's friends to theparty. The number of friends is a compositemultiple of her
son's age on his birthday. She has baked 48 cup cakes and each childwill receive
exactly the same number of cupcakes. Use your knowledge of factors and multiples
to find out how old her son will be on this birthday.

Answers

Answer:

48 cupcakes divided by the boys age equals amout of cupcakes per person.

Step-by-step explanation:


Asha is tiling the lobby of the school with one-foot square tiles. She has 6 bags
of tiles with 50 tiles in each. The lobby is a 30-foot by 8-foot rectangle. How
many tiles will Asha have left over after she tiles the lobby?

Answers

Answer:

60 tiles left over

Step-by-step explanation:

the lobby needs 30 x 8 = 240 tiles.

she has 6 x 50 = 300 tiles

300 - 240 = 60 left over

Calculate the SQRT485 Express answer to nearest hundredth.

Answers

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: 22.02

Explanation:

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Convince yourself that there are 3 similar triangles in the diagram. Choose the
similarity statement that represents the relationship among the 3 triangles.
Please only answer if your sure

Answers

The correct answer is the second option.

Answer:

second option.

Step-by-step explanation:

dilation of 1.5 about the origin

Answers

Answer:

Step-by-step explanation:

use the rule they tell you of  1.5

so (x,y) ⇔1.5(x,y)

w = (2,0)

x = ( 0,2)

y = (-2, 1)

z = (0, -2)

1.5(x,y)

W' = (3,0)

X'= (0, 3)

Y' = ( -3, 1.5)

Z' = (0, -3)

nice :)

what is the volume of the cylinder?
A:703.2ft3
B:50.2ft3
C:602.9ft3
D: 653.1ft3

Answers

The answer is A hope that helps

SOMEONE HELP ME PLEASE!!!!?

Answers

Answer:

139

Step-by-step explanation:

supplementary angles add up to equal 180

so to find the measure of angle ABC we subtract the given angle from 180

180-41=139

so we can conclude that angle ABC=  139

Step-by-step explanation:

< ABC and < CBD are supplementary angles.

< CBD = 41°

< ABC + < CBD = 180° ( Being supplementary angles)

< ABC + 41° = 180°

< ABC = 180° - 41°

< ABC = 139°

Hope it will help :)❤

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