An average scanned image occupies 0.5 megabytes of memory with a standard deviation of 0.2 megabytes. If you plan to publish 80 images on your web site, what is the probability that their total size is between 49 megabytes and 53 megabytes?

Answers

Answer 1

Answer:

Approximately [tex]0.012[/tex] (that's approximately [tex]1.2\%[/tex].)

Step-by-step explanation:

The question did not specify the exact distribution of the size of those images. However, the sample size [tex]n = 80[/tex] is a rather large number. Assume that:

the sizes of these [tex]80[/tex] images follow the same distribution, with mean [tex]\mu = 0.5[/tex] megabytes and standard deviation [tex]\sigma = 0.2[/tex] megabytes.the size of each image is independent of one another.

If both assumptions are met, the central limit theorem would apply. This theorem would suggest that the sum of the sizes of these [tex]80[/tex] image (a random variable) will approximately follow a normal distribution. The mean of that sum would be approximately [tex]n\cdot \mu= 80 \times 0.5[/tex]. The standard deviation of that sum would be approximately [tex]\sigma\, \sqrt{n} = 0.2\times \sqrt{80}[/tex].

Let [tex]\displaystyle \Sigma X[/tex] denote the sum of these eighty sizes.

Under these assumption, [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left(n\, \mu,\, \sigma\,\sqrt{n}\right)[/tex].

That is: [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left({80\times 0.5},\, \left(0.2\times \sqrt{80}\right)^2}\right)[/tex].

The question is asking for the probability [tex]P(49 \le \Sigma X \le 53)[/tex]. Therefore, calculate the [tex]z[/tex]-score that corresponding to [tex]\Sigma X = 49[/tex] and [tex]\Sigma X = 53[/tex]:

For [tex]\Sigma X = 49[/tex], the [tex]z[/tex]-score would be [tex]\displaystyle \frac{\sum X - n\, \mu}{\sigma \sqrt{n}} = \frac{49 - 80 \times 0.5}{0.2\times \sqrt{80}} = 2.25[/tex].For [tex]\Sigma X = 53[/tex], the [tex]z[/tex]-score would be [tex]\displaystyle \frac{\sum X - n\, \mu}{\sigma \sqrt{n}} = \frac{53 - 80 \times 0.5}{0.2\times \sqrt{80}} = 3.25[/tex].

Make use of a [tex]z[/tex]-table to find these two probabilities:

[tex]P(X \le 49) = P(Z < 2.25) \approx 0.98778[/tex].[tex]P(X \le 53) = P(Z < 3.25) \approx 0.99942[/tex].

Calculate the probability that this question is asking for:

[tex]\begin{aligned}& P(49 \le \Sigma X \le 53) \\ &= P(\Sigma X < 53) - P(\Sigma X < 49) \\ & \approx 0.99942 - 0.98778 \approx 0.012 = 1.2\%\end{aligned}[/tex].


Related Questions

please help!Thank you so much​

Answers

Answer:

An equation is a math sentence that DOES contain an equals sign (=).

The inverse of addition is subtraction.

The inverse of subtraction is addition.

The inverse of multiplication is division.

The inverse of division is multiplication.

Step-by-step explanation:

I'm sorry if I got the first one incorrect.

True or False. A triangle can be made with side lengths 4, 4 and 8.

Answers

Answer:

False

Step-by-step explanation:

In the parallelogram below,
z = [ ? ]°

Answers

Z is equal to 124 degrees

Evaluate p + 2 for p = -8.

Answers

Answer:

-6

Step-by-step explanation:

Which of the following statements about photocopier A1 is correct compared to the other photocopiers?

Answers

Answer:

Option 2

Step-by-step explanation:

Number of breakdowns of the photocopiers in year 2011,

A1 = 15

A2 = 21

B1 = 34

B2 = 32

B3 = 23

Option (1)

A1 had just under a half the number of breakdowns compared to photocopier B3.

Half of B3 = 12

And A1 = 15

Therefore, A1 > B3

So the statement is False.

Option (2)

A1 had just under 50% of the breakdowns compared to photocopier B2

50% of the breakdowns of B2 = 16

A1 = 15

So, A1 < 50% of B2

Statement (2) is True.

Option (3)

A1 had more than 25 extra breakdowns compared to B1.

A1= 15

B1 = 34

A1 < B1

Therefore, statement is False.

Option (4)

A1 had 6% less breakdowns than photocopier A2.

A1 = 15

A2 = 21

A2 - A1 = 21 - 15 = 6

Percentage less breakdowns = [tex]\frac{6}{21}\times 100[/tex] = 28.6%

So this Option is False.

Therefore, Option (2) is the correct option.



Find the Lateral Area
A triangular prism and its dimensions are shown in the diagram.
5 cm
5 cm
8 cm
6 cm
What is the lateral surface area of this triangular prism in square centimeters?

Answers

Answer:

? please explain

Step-by-step explanation:

Answer:128 I think is the answer

Step-by-step explanation:

5. What are the dimensions of this matrix?
Please help meeeeeeeeeee

Answers

Answer:

4 x 1

Step-by-step explanation:

The matrix shown in the illustration has 4 rows and 1 column, and thus we give the dimensions as 4 x 1.

Helpppp pleaseeeeeeee

Answers

Answer:

x= 6.85 or 89/13

Step-by-step explanation:

perimeter is sum of all sides added, so add them all and set them equal to 84

4(x-3) + 3x - 1 + 6x + 8 = 84

distribute

4x + 12 + 3x - 1 + 6x + 8 = 84

combine like terms

13x - 5 = 84

solve for x

x = 89/13 = 6.85

Find the unit rate. Round to the nearest hundredth, if necessary.

$5.99 for 12 lb

Answers

(Around) 50 cents. If you round 5.99 to 6.00 and divide by 12, you get 50. But if you want more of an exact answer, it’s 0.4991666667 (and if you round, you get 0.50 either way)

HELP FASTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT

Answers

Answer:

Step-by-step explanation:

 U bot. Nub

help plz very very confused

Answers

Answer:

x=-2

Step-by-step explanation:

4. Write as a fraction in simplest form: 38 minutes to 12 minutes

Answers

Answer:

3 ⅙

Step-by-step explanation:

38 and 12’s common factor would be 2. Now the fraction is 19/6.

How many 6’s can fit into 19? 3. With a remainder of 1 we have:

3 ⅙

2. Which of the following is the correct value of (0.22) - (0.4)? Show your reasoning. c. 0.088 d. 0.0088 w​

Answers

Answer:

C

Step-by-step explanation:

there would have to be one more zero between 0 and 8 for both of them

HELP ASAP PLEASE!!! senora need 300 grams of a spice mix to put in her pasta dish. The store sells the spice mix by the ounce. there are approximately 28.35 grams in 1 ounce how many ounces of spice mix does senora need, rounded to the nearest hundredth?

Answers

Answer: 3,969

Step-by-step explanation:

multiply 140x28.35

Perform the indicated operation.
1 1/7x 2 4/5

Answers

Explanation: none




Answer: The answer would be 3.2

The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years. a. Find the probability that a cat will live to be older than 14 years. b. Find the probability that a cat will live between 14 and 18 years. c. If a cat lives to be over 18 years, would that be unusual? Why or why not? d. How old would a cat have to be to be older than 90% of other cats?

Answers

Answer

a. 0.856

b. 0.78071

c. It is not unusual

d. 13.65 years old

Step-by-step explanation:

The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years.

We solve this question using z score formula:

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

a. Find the probability that a cat will live to be older than 14 years.

For x > 14 years

z = 14 - 15.7/1.6

z = -1.0625

Probability value from Z-Table:

P(x<14) = 0.144

P(x>14) = 1 - P(x<14) = 0.856

b. Find the probability that a cat will live between 14 and 18 years.

For x = 14 years

z = 14 - 15.7/1.6

z = -1.0625

Probability value from Z-Table:

P(x = 14) = 0.144

For x = 18 years

z = 18 - 15.7/1.6

z= 1.4375

Probability value from Z-Table:

P(x = 18) = 0.92471

The probability that a cat will live between 14 and 18 years is calculated as:

P(x = 18) - P(x = 14)

0.92471 - 0.144

= 0.78071

c. If a cat lives to be over 18 years, would that be unusual? Why or why not?

For x > 18 years

z = 18 - 15.7/1.6

z= 1.4375

Probability value from Z-Table:

P(x<18) = 0.92471

P(x>18) = 1 - P(x<18) = 0.075288

Converting this to percentage:

0.075288 × 100 = 7.5288%

Hence, 7.5288% of the cats live to be over 18 years. Hence, it is not unusual.

d. How old would a cat have to be to be older than 90% of other cats?

From the question above, 10% of the cats would be older than 90% of other cats.

Hence, we find the z score of the 10th percentile

= -1.282

Hence,

-1.282 = x - 15.7/1.6

Cross Multiply

-1.282 × 1.6 = x - 15.7

- 2.0512 = x - 15.7

x = 15.7 -2.0512

x = 13.6488 years old

Approximately = 13.65 years old

Plz help with question

Answers

Answer:

I believe it's B

Step-by-step explanation:

Isosceles triangles have congruent base angles, so base angle A and B should both be the same number. (25)

Added up, 25+25+130 is 180 degrees.

You run 6 miles in one hour and 24 miles in four hours.
a. 6 miles
per hour
c. 4 hours
b. 4 miles per hour
d. 6 miles

Answers

Answer:b

Step-by-step explanation:

A is carrect 24/4 6 mile

Write the following in standard form: eight and twelve thousandths.

Answers

Answer:

8.012

Step-by-step explanation:

standard : 8.012

written: eight and twelve thousandths.

8.012 hopes this helps

DATE
PERIOD
Unit 3, Lesson 7: Cool-down
M
7.5: Cheetah Speed
(2 4
A cheetah can run at its top speed for about 25 seconds. Complete the table to represent a cheetah
running at a constant speed. Explain or show your reasoning.
time (seconds) distance (meters) speed (meters per second)
4
120
25
270

Answers

Answer:

ok this was a good one so here

Step-by-step explanation:

time (seconds)

distance (meters)

speed (meters per second)

4 120 30

25 750 30

9 270 30

The required values are in the completed table which has been attached below.

What is the distance?

Distance is defined as the product of speed and time.

Since the Cheetah's speed is constant, the speed must be consistent throughout the table.

To calculate the unknown time and distance, use the following formula:

Speed = Distance/Time = c

When distance = 120m, time = 4 secs

Speed = 120/4 = c

Speed = 30m/s = c

We are to get the distance when the time is 25 secs

Speed = Distance/Time

30 = d₂/25

d₂ = 30 × 25

d₂ = 750 m

To get the time in the third column

Time = Distance/Speed

t₃ = 270/30

t₃ = 9seconds

Therefore, the required values are in the completed table which has been attached below.

Learn more about the distance here:

brainly.com/question/13269893

#SPJ2

what the answer?please tell me
12 points

Answers

Step-by-step explanation:

[7 + (-2)] * (-3)

= 7(-3) + (-2)(-3)

= -21 + 6

= -15. (C)

Answer:

C. -15

Step-by-step explanation:

Hope this helped have an amazing day!

Help thank you to who ever does I will mark brainliest.

Answers

Answer:

V = 200.96 units ^3

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h

The radius is  4 and the height is 12

V = 1/3 ( 3.14 ) ( 4)^2 * 12

V = 200.96 units ^3

ANSWER:  200.96 units

what does the dot (.) stand for in math

Answers

The dot stands for multiplication for example
4 •6 = 24 same as 4x6=24






If you’re talking about decimals

It is a point or dot we use to separate the whole number part from the fractional part of a decimal number. ... The decimal point separates the whole number from the fractional part. Example: In the number 257.16, the decimal point separates the whole number 257 from the fractional part 16, which is 16 hundredths.

Answer:

The dot is called a decimal. Its what separates the whole number and the fraction of the number.

Step-by-step explanation:

For example, 0.5 is saying half, or 50 out of 100.

1) What is the constant of proportionality that relates y to x
х
Y
8
6
20
15
28
21
a. 1.33
6,48
0.0.75
b. 14
f

Answers

Answer:  The Answer Is A Because if u just add the numbers then divide them

Help I on my have 10 minutes!!!PLZZZZZX

Answers

what’s the question?

What if it is asking you to divide and not multiply?

Answers

Answer:

Then you divide :)

<3 Enjoy,

    Dea

4. -5x-15=-3x+23
29. -107-7x=73-13x
EXPLAIN STEPS AND SHOW WORK
THANKS BROTHA
`•••~Low_Millenial~•••`
°°°°°°Tutor and pal°°°°°°°​

Answers

Answer:

x=-19  x=30

Step-by-step explanation:

-5x-15=-3x+23

    -23      -23

-5x-38=-3x

+5x        +5x

-38=2x

/2       /2

-19=x

-107-7x=73-13x

-73         -73

-180-7x=-13x

      +7x   +7x

-180=-6x

30=x

Which expressions are equivalent to 4• (7 • y)?

Drag and drop the equivalent expressions into the box.

(7• y)• 4

4 • 7 + 4 • Y

(4 7 • y

28 y

4•7•4• y

PLEASE HELP ASAP!!!
50 POINTS AND BRAINLY!!

Answers

Answer:

Step-by-step explanation:

4• (7 • y) is equivalent to all of the following:

28 • y

4 · 7y or (4 · 7) · y

(7 · 4) · y

Note that 4 • 7 + 4 • Y is absolutely wrong, since the original expression has no " + " sign

Factorise 3x to the power of 2 + xy

Answers

Answer:

 x • (3x + y)

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x to the power of to +xy= x (3x+y)

Determine whether the functions f(x) = -7/5x +4/5 and g(x) = x – 4 intersect at x = 2.

A.No, because f (2) #g(2) when r =
B. No, because f (0) = 9(2) when I = 2.
C. Yes, because f(x) + 9(2) when r = 2.
D. Yes, because f(x) = 9(2) when I = 2.​

Answers

Answer:

D. Yes, because f(x) = g(x) when x = 2.​

Step-by-step explanation:

Given the functions f(x) = -7/5x +4/5 and g(x) = x – 4, for the functions to intersect, f(x) must be equal to g(x) i.e f(x) = g(x) at x = 2

-7/5x +4/5= x- 4

If x = 2

f(2) = -7/5 (2)+ 4/5

f(2) = -14/5 + 4/5

f(2) = -10/5

f(2) = -2

g(x) = x - 4

g(2) = 2-4

g(2) = -2

Since f(2) = g(2), hence the lines intersects at x = 2

Answer:  abidemiokin is ritgh

Step-by-step explanation:

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