the mean of 200 item was 50 later on it was found that two items were wrongly taken as 92 and 8 instead of 192 and 88 find the correct mean.​

Answer:

a) The mean is 10 and the variance is 0.0625.

b) 0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.

c) 10.58 minutes.

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Normally distributed with a mean of 10 minutes and a standard deviation of 2 minutes.

This means that [tex]\mu = 10, \sigma = 2[/tex]

Suppose 64 visitors independently view the site.

This means that [tex]n = 64,  = \frac{2}{\sqrt{64}} = 0.25[/tex]

a. The expected value and the variance of the mean time of the visitors.

Using the Central Limit Theorem, mean of 10 and variance of (0.25)^2 = 0.0625.

b. The probability that the mean time of the visitors is within 15 seconds of 10 minutes.

15 seconds = 15/60 = 0.25 minutes, so between 9.75 and 10.25 seconds, which is the p-value of Z when X = 10.25 subtracted by the p-value of Z when X = 9.75.

X = 10.25

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

By the Central Limit Theorem

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

[tex]Z = \frac{10.25 - 10}{0.25}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.8413.

X = 9.75

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

[tex]Z = \frac{9.75 - 10}{0.25}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826.

0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.

c. The value exceeded by the mean time of the visitors with probability 0.01.

The 100 - 1 = 99th percentile, which is X when Z has a p-value of 0.99, so X when Z = 2.327.

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

[tex]2.327 = \frac{X - 10}{0.25}[/tex]

[tex]X - 10 = 2.327*0.25[/tex]

[tex]X = 10.58[/tex]

So 10.58 minutes.

9514 1404 393

Answer:

  3x

Step-by-step explanation:

If x represents the number, then "3 times a number" is 3x.

__

Additional comment

"The quotient of the number and 4" is x/4.

The sum of those two expressions is ...

  3x + x/4

Answer:

te qif y btubf

Step-by-step explanation:

Answer:

0.0728177272

Step-by-step explanation:

Given :

Number of flips = 80

Probability of landing on tail at most 33 times ;

Probability of landing on tail on any given flip = 1 / 2 = 0.5

This a binomial probability problem:

Hence ;

P(x ≤ 33) = p(x=0) + p(x=1) +... + p(x = 33)

Using a binomial probability calculator :

P(x ≤ 33) = 0.0728177272

Answer:

We can construct a 90º angle either by bisecting a straight angle or using the following steps.

Step 1: Draw the arm PA.

Step 2: Place the point of the compass at P and draw an arc that cuts the arm at Q.

Step 3: Place the point of the compass at Q and draw an arc of radius PQ that cuts the arc drawn in Step 2 at R.

Step-by-step explanation:

Answer:

A. -510

Step-by-step explanation:

We are given the variable values:

Geometric series formula:

[tex]s = \frac{a( {r}^{n} \times - 1) }{r - 1} [/tex]

Plugging in values we have:

[tex]s = \frac{ - 2( {2}^{8} - 1) }{2 - 1} [/tex]

Simplifying the equation we are left with:

[tex] \frac{ - 2(255)}{1} = - 510[/tex]

Answer:

12.9 miles

Step-by-step explanation:

Formula: (x/360)×dπ(circumference)

90/360=1/4

1/4×16.4π

1/4×51.496

12.874

Answer:

[tex]m JM=90 =\Theta[/tex]

[tex]Radius=dimeter/2=16.4/2[/tex]

[tex]\longrightarrowr=8.2[/tex]

The length of arc JM=

[tex]=\frac{\Theta }{360} \times\pi r[/tex]

[tex]=\frac{90}{360} \times2\times\ 3.14\times 8.2[/tex]

[tex]=12.874[/tex]

[tex]\approx 12.9 \; miles[/tex]

[tex]OAmalOHopeO[/tex]

Answer:

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

78

Answer:

-243

Step-by-step explanation:

(-3) (-3) (-3) (-3) (-3) = - 243

[tex]\frac{1}{-243 }[/tex]

Answer:

Option D

Step-by-step explanation:

Generally the equation for Margin of Error is mathematically given by

[tex]M.E=Z*sqrt{\frac{p*(1-p)}{n}}[/tex]

Condition for Largest M.E

n has to be smallest and Z value has to be largest.

Where

From options

Smallest [tex]n=300[/tex]

Largest Z value respects to [tex]\alpha=95\%[/tex]

Therefore

n= 300, confidence level 95%

Option D

Answer:

mean=256229+253657+218747+246163+235626+288694+316265+196721+285077+215152+253291+315011+199901+265443+291806+303556+215359+258554+293658+289935÷21

=5198845÷21

=247564.0

=247564 to the next whole number

B.6 times

Answer:

84.5

Step-by-step explanation:

Given :

Mean μ = 80

Standard deviation, σ = 5

Z = number of standard deviations from the mean, Z = 0.9

Teat score, x

Using the Zscore formula :

Zscore = (x - μ) / σ

Plugging in our values :

0.9 = (x - 80) / 5

Cross multiply

0.9 * 5 = x - 80

4.5 = x - 80

4.5 + 80 = x

x = 84.5

Test score = 84.5

3 | x - 7 | = 15

Divide both sides by 3

3 | x - 7 | ÷ 3 = 15 ÷ 3

| x - 7 | = 5

_________________________

" Reminder "

| a | = t ===》 a = + t OR a = - t

__________________________

| x - 7 | = 5

x - 7 = 5 ====》 x = 12

OR

x - 7 = - 5 ===》 x = 2

Answer:

13.5% is the increase in percentage

Answer:

74%

Step-by-step explanation:

To get the answer, divide 800 by 1080, and you will get a decimal. That decimal is 0.74074074074. Then, move the decimal point two times two the right, so you should have 074.074074074. Ignore everything after the decimal point as well as the 0 before the decimal point, and if done correctly, it should be 74%.

So, the final answer would be 74%.

Hope this helped!

Answer:

She only has 120 croat

Step-by-step explanation:

We can use a ratio to solve

She only has 20 dollars

1 dollar     20 dollars

----------  = --------------

6 croat     x croat

6*20 = x

120 =x

120croat

She does not have enough money

She needs 138 croat

Answer:

120 croatian kuna

Step-by-step explanation:

Answer:

Terminal point for 4π/3

(cos4π/3 ,sin4π/3)

{cos(π+π/3) ,sin(π+π/3)}= (-cosπ/3 ,-sinπ/3)

or ,(- 1/2, -√3/2)

OPTION C

Answer:

f(0) = 2

f(x) = 4x + 2

Step-by-step explanation:

You can see that the consecutive x-values are producing y-values that increase by 4 each time. Since the change in y is the same every time, we know this is a linear graph because in a continuous linear graph the slope does not change.

We can use the equation for a line: y = mx + b,

where m is the slope and b is the y-intercept.

The slope [m] is calculated by [change in y]/[change in x]. The y-values are increasing by 4 each time x increases by 1. m = 4/1 = 4.

Once we have found the slope, we can find the value for f(0). The line graph has a positive slope, so to find the value at x=0, we would subtract 4, moving backwards along the line.

6-4 = 2

The y-intercept on a line is the y-value for which x = 0. In this case we have already solved for the y-intercept, f(0) = 2.

Now plug the values into the formula.

y = mx + b

The value of f(0) is 2.

The equation of this linear function is y = 4x + 2

A function is defined as a relation between a set of inputs having one output each.

The inputs are called domain of the function.

The outputs are called the range of the function.

We have,

x = 1, 2, 3, 4

f(x) = 6, 10, 14, 18

The f(x) values are the values we get when we substitute x values.

There is a difference of 4 in the f(x) values.

10 - 6 = 4

14 - 10 = 4

18 - 14 = 4

Since the difference between the values of f(x) is same, the given function is a linear function.

The equation of this linear function will be in the form of:

y = mx + c

m = slope

c = y-intercept

Find m.

Choose any two points as: (1, 6) and (2, 10)

m = 10-6 / 2-1 = 4/1= 4

Find c.

x = 0 in y-intercept and choosing any point = (1, 6)

So,

6 = 4 + c

c = 6 - 4 = 2

Now,

The equation of this linear function:

y = 4x + 2

f(0) = 4 x 0 + 2 = 0 + 2 = 2

Thus,

The value of f(0) is 2.

The equation of this linear function is y = 4x + 2

Learn more about functions here:

brainly.com/question/17440903

#SPJ2

Answer:

Step-by-step explanation:

One solution, at the point of intersection, (3,3)

Answer:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

Step-by-step explanation:

Hi there!

Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope

1) Determine the slope

[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-2, 6) and (3,-2):

[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]

Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

2) Plug in a point [tex](x_1,y_1)[/tex]

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

I hope this helps!

Answer:

0.2358 = 23.58% probability that at least 18 of the 75 sampled employees would like to move into management.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed 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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

20% of employees would like to move into management and be the boss.

This means that [tex]p  = 0.2[/tex]

Sample of 75:

This means that [tex]n = 75[/tex]

Mean and standard deviation:

[tex]\mu = E(X) = np = 75(0.2) = 15[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{75*0.2*0.8} = 3.4641[/tex]

Find the probability that at least 18 of the 75 sampled employees would like to move into management.

Using continuity correction, this is [tex]P(X \geq 18 - 0.5) = P(X \geq 17.5)[/tex], which is 1 subtracted by the p-value of X = 17.5. So

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

[tex]Z = \frac{17.5 - 15}{3.4641}[/tex]

[tex]Z = 0.72[/tex]

[tex]Z = 0.72[/tex] has a p-value of 0.7642.

1 - 0.7642 = 0.2358

0.2358 = 23.58% probability that at least 18 of the 75 sampled employees would like to move into management.

Answer:

Hari saves $ 10,320 in a year.

Step-by-step explanation:

Given that Hari earns $ 4300 per month, and he spends 80% from his income, to determine how much amount does he save in a year, the following calculation must be performed:

100 - 80 = 20

4300 x 0.20 x 12 = X

860 x 12 = X

10320 = X

Therefore, Hari saves $ 10,320 in a year.

Answer:

3/ 7

Step-by-step explanation:

We know that it is an even ball

2,4,6,8,10,12,14 are even balls

2,4,6,8 are red and 10,12,14 are white

P ( white) = white even / total even

              = 3/ 7

Answer:

x=37.84

Step-by-step explanation:

We can write a ratio to solve

4 gallons        11 gallons

--------------- = ----------------

13.76              x dollars

Using cross products

4x = 11*13.76

4x=151.36

Divide by 4

4x/4 = 151.36/4

x=37.84

Answer: the numbers are 10 and 5

Step-by-step explanation:

10 times 5 is 50

10 plus 5 is 15

Answer:

[tex]{ \tt{6x + 5 = - 29}} \\ { \tt{6x = - 36}} \\ { \tt{x = - 6}}[/tex]

Answer:

-3x^2 +7x -4

-------------------------------

(x-3)(x-2)(x+3)

Step-by-step explanation:

2              3x

--------   - ----------

X^2-9    x^2 -5x+6

Factor

2                 3x

--------   -      ----------

(x-3)(x+3)   (x-3)(x-2)

Get a common denominator

2  (x-2)               3x(x+3)

--------   -             ----------

(x-3)(x+3)(x-2)   (x-3)(x-2)(x+3)

2x-4  - (3x^2 -9x)

-------------------------------

(x-3)(x-2)(x+3)

Distribute

2x-4  - 3x^2 +9x

-------------------------------

(x-3)(x-2)(x+3)

Combine like terms

-3x^2 +7x -4

-------------------------------

(x-3)(x-2)(x+3)

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