The following data represent the​ high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population. Complete parts​ (a) through​ (c).

Temperature Lower Limit Upper Limit Days
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9

Required:
Approximate the mean and standard deviation for temperature.

Answers

Answer 1

Answer:

The mean is  [tex]\= x  = 79.7 [/tex]

The standard deviation  [tex]\sigma =7.81[/tex]

Step-by-step explanation:

From the question we are told that

  The data given is  

Temperature                Lower Limit           Upper Limit               Days

50-59                               50                             59                          2

60-69                                 60                            69                        313

70-79                                  70                           79                          1419

80-89                                   80                          89                         1503

90-99                                   90                          99                          319

100-109                                100                         109                         9        

Generally the average of each limit is evaluated as

Temperature    Lower Limit   Upper Limit         Average[tex](x_i)[/tex]                    Days[tex](f_i)[/tex]

50-59                 50                   59              ( 50 + 59 )/2 =54.5                 2

60-69                 60                   69              (60+69)/2 = 64.5                    313

70-79                 70                    79               (70+79)/2 =74.5                    1419

80-89                 80                   89                (80+89)/2 =84.5                  1503

90-99                 90                   99                 (90+99)/2 = 94.5                319

100-109             100                  109                 (100+109)/2 = 104.5            9  

Generally the mean is  evaluated as

     [tex]\mu  =  \frac{\sum x_i f_i}{\sum f_i}[/tex]

=>  [tex]\mu  =  \frac{ (54.5 * 2) + (64.5 * 313) +\cdots +(104.5 *  9)}{2 + 313 +\cdots + 9}[/tex]

=> [tex]\= x  = 79.7 [/tex]

Generally the standard deviation  is  evaluated as

    [tex]\sigma = \sqrt{ \frac{\sum[ f_i * ( x_i^2 - \= x^2)] }{\sum f_i}}[/tex]

=>   [tex]\sigma =\sqrt{ \frac{[2 * [(54.5)^2) - 79.7^2 ]]+[313 *[ (64.5)^2)-79.7^2] +\cdots +[9 *[ (104.5)^2)- 79.7^2]  }{2 + 313 +\cdots + 9}}[/tex]

=>  [tex]\sigma =7.81[/tex]

   

Answer 2

The mean and Standard deviation for the given data would be as follows:

μ [tex]= 79.7[/tex]

б [tex]= 7.81[/tex]

Frequency Distribution

Given that,

Temperature       Lower Limit           Upper Limit             Days([tex]f_{i}[/tex])

50-59                       50                           59                          2

60-69                       60                           69                         313

70-79                         70                           79                          1419

80-89                        80                          89                          1503

90-99                        90                          99                           319

100-109                    100                         109                            9  

Average([tex]x_{i}[/tex])    

[tex]( 50 + 59 )/2 =54.5[/tex]

[tex](60+69)/2 = 64.5[/tex]

[tex](70+79)/2 =74.5[/tex]

[tex](80+89)/2 =84.5[/tex]

[tex](90+99)/2 = 94.5[/tex]

[tex](100+109)/2 = 104.5[/tex]

As we know,

Mean (μ) [tex]=[/tex] ∑[tex](x_{i} f_{i}) /[/tex]∑[tex]f_{i}[/tex]

[tex]= [(54.5[/tex] × [tex]2) + (64.5[/tex] ×[tex]313)+....(104.5[/tex]× [tex]9)][/tex][tex]/(2 + 313 + 1419 + ....9)[/tex]

∵ μ [tex]= 79.7[/tex]

As we know,

Standard Deviation:-

[tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{f_{i} }}}[/tex]

by putting the values, we get

∵ б [tex]= 7.81[/tex]

Thus, μ [tex]= 79.7[/tex] and б [tex]= 7.81[/tex] are the correct answers.

Learn more about "Temperature" here:

brainly.com/question/7510619


Related Questions

Find the area and perimeter of a rectangle whose sides are √2 + 3 √5 + 2

Answers

Answer:

√10 + 2√2 + 3√5 + 6

2√2 + 2√5 + 10

Step-by-step explanation:

Given parameters:

Dimensions of the rectangle:

         √2 + 3  and √5 + 2

Unknown:

Area and Perimeter of the rectangle  = ?

Solution:

  Area of a rectangle = L x W

   Perimeter of a rectangle = 2 (L + W)

Input the parameters and solve;

     Area = (√2 + 3)(√5 + 2)

             = √10 + 2√2 + 3√5 + 6

   Perimeter of a rectangle  = 2(√2 + 3 + √5 + 2)

                                            = 2√2 + 6 + 2√5 + 4

                                           = 2√2 + 2√5 + 10

is 3.4567 irrational or rtional

Answers

3.4567 is irrational

Answer:

3.4567 is a rational number

Step-by-step explanation:

An irrational number has no ending while a rational number does. An irrational number can not be written as a fraction while a rational number can. Basically, all you have to do to figure out if a number is rational or irrational is to figure out if it has an ending.

For example, if you had 234.888888888 irrational but if the number was 234.98989654 then it would be rational

A coin is about to be tossed 50 times. Determine the probability the 8th heads occurs on the 12th toss

Answers

Answer:

0.0806

Step-by-step explanation:

From the given information:

Number of toss = 50

The probability of having a head = 1/2 = 0.5

The Probability of 8th head occur on 12th toss can be computed as :

Pr(8th head occur on 12th toss) = Pr(7 heads in 11 toss) × P(8th head on 12th toss)

Pr(8th head occur on 12th toss) =  C(11,7) × 0.5⁷ × (1 - 0.5)⁴ * 0.5

Pr(8th head occur on 12th toss) = [tex]\dfrac{11!}{7!(11-7)!}[/tex] × 0.5⁷ × (1 - 0.5)⁴ × 0.5

Pr(8th head occur on 12th toss) =  0.0806

Answer:

The probability of 8th heads,

That is occurred on 12th toss.

Step-by-step explanation:

A coin is tossed 50 times.

There are two possible outcomes of occurring a head or tail.

Probability of occurring head = no.of head/ possible outcomes

                                                    = 1/2

Total number of tossing a coin= 50 times

Probability of 8th heads occurs on 12th toss:

                                                         12C8 (1/2)8 (1/2)9 (1/2)10 (1/2)11 (1/2)12

                                 =         12C8  (1/2)8+9+10+11+12

                                                    = 12C8  (1/2)50

                                  = 12C8   / 250

                                                       = 495 / 1125899906842624

                                  = 4396.48317752 x 10-16

This is the probability of 8th heads,

That is occurred on 12th toss.

What is the slope of the equation of this line? (Put into y=mx+b form first). 6x+y=-1

Answers

Answer:

-6

Step-by-step explanation:

6x + y = -1

y = -6x-1

slope which is m is -6

What operation is happening in an additive pattern??

Multiplication
Subtraction
Addition
Division

Answers

Answer:

Addition

Step-by-step explanation:

If it has the word "add" in it it's probably addition.

Answer:

The answer is addition.

Step-by-step explanation:

Find the slope of the line y=-3x+3

Answers

Answer:

Step-by-step explanation:

M = -3

y= mx +b

m stands for slope and -3 is in that position so -3 is your slope

Answer:

⇝ Slope = -3

Step-by-step explanation:

The question is asking us to find the slope of the line y = -3x + 3.

Note that the equation is written in slope-intercept form:

y = mx + b

Where:

m = slope (coefficient of x)b = y-intercept (constant)

For this problem the coefficient of x is -3, and the constant is 3.

Therefore, the slope is -3.

How many sandwiches must you sell to make $100 profit

Answers

Answer:

About 25 sandwiches...

Step-by-step explanation:

Answer:

67 sandwiches

Step-by-step explanation:

If you invest 250 dollars to start, you're currently -250. If you gain 5.25 per sandwich you sell, you'd need to sell about 67 sandwiches.

I'm not entirely sure what your question meant though. If the question is simply asking how many sandwiches it would take to make 100 dollars, it would be about 20 sandwiches. If the question is asking how many sandwiches you'd need to sell to gain 100 dollars in profit, covering the cost of the cart, it would be about 67 sandwiches.

what is the answer the question 3? pls help!!

Answers

Answer:

no slope

Step-by-step explanation:

m=y2-y1/x2-x1

(-1)-1=(-2)

7-7=0

(-2)/0 is undifined

there is no slope

hope this helps :3

Your economics instructor assigns you and a student you do not know a joint project. Assume that you and your partner are both interested in maximizing your grade, but you are both very busy and get more happiness if you can get a good grade with less work. Since you do not know the student, making a credible commitment to how much you are going to work is impossible. Note that on the payoff matrix below, 10/10 is happiest and 1/10 is least happy. This level of happiness is a combination of how much you work and the grade you achieve. Assume that you will have to work on only one project with this partner.
You Work Hard Work Less Hard Grade-A, but you had to work 6 hours. Happiness-6/10 [Grade A, and you only worked 2 hours. Happiness-10/10 Your Partner Work Har Grade-A, but your partner had to work 6 hours. Happiness-6/10 Grade-A, but your partner had to work 10 hours. Happiness 4/10 Work Less Hard Grade-A, but you had to work 10 hours. Happiness-3/10 Grade B, but you only worked 4 hours. Happiness 5/10 Grade A, and your partner only worked 2 hours. Happiness-8/10 Grade- B, but your partner only worked 4 hours. Happiness-5/10 In this game, both you and your partner will collectively work a total of hours on the project.

Answers

Answer:

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Step-by-step explanation:

is 1.05 a terminating decimal

Answers

Answer:

No

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Aniya is helping her father paint a fence. She can paint 2 sections of the fence in 15 minutes. How many minutes will it take Aniya to paint 12 sections of the fence.

Answers

Answer:

90 minutes

Step-by-step explanation:

Since 15 divided by 2 is 7.5, it takes 7.5 minutes to paint 1 section. 7.5 times 12 is 90, meaning that is takes 90 minutes for her to paint 12 sections.

Trevor paints 1/6 of the fence surrounding his farm each day how many days will it take him to paint 3/4 of the fence?

Answers

Answer:

5 days

Step-by-step explanation:

1/6 = 2/12

3/4 = 9/12

9/2=4.5

rounded 5

The correct Standard Form of the equation y=−2/7x−11/7

Answers

Answer:

y=-(2)/(7)x-5

Step-by-step explanation:

i mark as brainliest ​

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I want to say 6.75 just because it's to small tho

Step-by-step explanation:

Answer:It's -6.75 because you can see the halfway point and how the dot is closer to -7 than -6 meaning it's bigger than -6.5

Step-by-step explanation:

solve the following equation for a: -g + 3/4a = y

Answers

9514 1404 393

Answer:

  a = (4/3)(y+g)

Step-by-step explanation:

Isolate 'a' term, then multiply by the reciprocal of its coefficient.

  [tex]-g+\dfrac{3}{4}a=y\qquad\text{given}\\\\\dfrac{3}{4}a=y+g\qquad\text{add $g$}\\\\\boxed{a=\dfrac{4(y+g)}{3}}\qquad\text{multiply by $4/3$}[/tex]

Evaluate 8 ÷ -2 · 4²+9. Thanks! Will give brainiest if possible

Answers

the answer is -55 , because you have to simply the 14^2 to 16
For more anwsers for questions like these use math away love even thought the ads might be irritating it’s a great source ✨

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Answers

Answer:

it doesn't because it's not a set of ordered pairs

Identify the holes, vertical asymptotes, and horizontal asymptotes of the following.


[tex]f (x) = \frac{2}{x-3}[/tex]

Answers

Answer:

Horizontal asymptote: y = 0

Vertical asymptote: x = 3

Step-by-step explanation:

The vertical asymptote in this graph would be when x = 3 because it would make the denominator 0, which would make the equation undefined.

There will not be any holes in the graph, because there won't be any point undefined in the function except for when x = 3, but that's a vertical asymptote.

Now, for the horizontal asymptote, we see what value y approaches as x approaches plus and minus infinity. Since x is in the denominator, y will approach 0 when it's plus or minus infinity.

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Vertical asymptote: x = 3

What is a reasonable estimate of -3 4/5 + (-5.25) and the actual value?​

Answers

Answer:

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Step-by-step explanation:

A fashion designer wants to know how many new dresses women buy each year. Assume a previous study found the standard deviation to be 1.3. He thinks the mean is 5.5 dresses per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.1 at the 95% level of confidence? Round your answer up to the next integer.

Answers

Answer:

649

Step-by-step explanation:

Given that

Mean number of dresses is 5.5

Standard deviation of the sample, S.D is 1.3

Margin of error, M.E is 0.1

Level of confidence is 95% or 0.95

The formula for margin of error, M.E is

Z * (S.D/√n) , where

Z = Value for level of confidence which is 1.96

Proceeding further, we have

0.1 = 1.96 * (1.3/√n)

0.1 = 2.548 / √n, making √n subject of formula, we have

√n = 2.548 / 0.1

√n = 25.48, squaring both sides

n = 25.48²

n = 649.23

Therefore the number of sample size we're looking for is n = 649.23, when rounded to the nearest integer, we have it to be 649

What is the inverse of the function? *
f(x)=3x+1

Answers

Answer:

The inverse of f(x)=3x+1 is f(x)−1=13x−13

Step-by-step explanation:

Answer:

[tex]f(x)^{-1} = \frac{1}{3}x - \frac{1}{3}[/tex]

Step-by-step explanation:

Inverse means the opposite of the original function.

I need help I don't understand ​

Answers

The answer is $10.25

Answer:

96.9

Step-by-step explanation:

A little bit of this and allit;e bit of that

How many milliters are in 90 ounces

Answers

Answer:

2661,62 ml

Step-by-step explanation:

can i plz have brainliest :)

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Answers

the measurement should be 4

Simplify the algebraic expression by combining like (or similar) terms.
5+9x+2

Answers

Answer:

7 + 9x

Step-by-step explanation:

add 5 and 2 and 9x doesn't have a like term so it stays the same

Answer:

9x + 7

Step-by-step explanation:

Like terms are terms that have the same variables and powers. Here, for 9x, there is no other term that is multiplied by x. So, the only terms we can combine is 2 and 5 which leaves us with 9x+7.

Given parallelogram ABCD, the measure of angle C

Answers

Answer:

70 is the answer to the question

Answer:

[tex]70^{o}[/tex]

Step-by-step explanation:

Opposite angles in a parallelogram are equal. The opposite angle to A is C and we are trying to find angle C. Therefore, <C = <A, therefore, <c= 70 degrees

whats 62.7×2.45......?

Answers

Answer:

153.615

Step-by-step explanation:

62.7 × 2.45=153.615

Alice has x dollars in her bank account. She deposits $75 in her account. After the deposit, the account has $550. Write an equation that could be used to figure out how much money was in her account before the deposit.

Answers

Answer:

$475

Step-by-step explanation:

$550 - $75 = $475

$475 = x

Answer:

The answer would be  $550-$75

Step-by-step explanation:

This would give you how much money was in her account before she adds the deposit.

Which inequality is true?

Answers

Answer:

8 pi > 24  true

Step-by-step explanation:

12/pi >4

12 > 4pi

pi is slight greater than 3

12 > 4* a number greater than 3

12 >  a number greater than 12  false

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a number slightly greater than 3 + 3 < 6

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8 pi > 24

8 * a number slightly greater than 3 > 24

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6 - a number slightly greater than 3 > 3

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iiii need heeelllppp with this one

Answers

Step-by-step explanation:

line passes through the point (5,0) and another one (0,3)

equation of the line passing through two points is

x-x1/x2-x1=y-y1/y2-y1

so

x-5/0-5=y-0/3-0

(x-5)*3=y*(-5)

3x-15+5y=0

this is the equation of the line shown in the graph

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