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3 years ago

Remove a number from the following data set so the mean is 20. 10, 12, 20, 23, 25

Mathematics

1 answer:

Nesterboy [21]3 years ago

4 0

Answer:

Take £ to be sigma

mean=£fx/£f

This means the sum of the digits divided by the number of digits

So from the above question 10+12+20+23+25=90 but 90 - 10 = 80

And 80 divided by 4 is 20

therefore the mean is 20.

Step-by-step explanation:

First of all, since the sum of the above digits is 90, we would need to exclude one of the above digits to make the number, a number divisible by 4( since we have excluded one of the 5 digits to make it 4 ) equal to 20.

So systematically, the equation would be defined as

x/4 = 20/1

hence we cross multiply and x becomes

x = 20 × 4

therefore x= 80

Hence, since x = 80 we divide this by our number of digits above hence giving you

80 ÷ 4 = 20

So from the above equation, we would need to exclude 10 to give us our mean of 20.

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In a recent survey, 60% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find

andreev551 [17]

Answer:

Probability that exactly 5 of them favor the building of the health center is 0.0408.

Step-by-step explanation:

We are given that in a recent survey, 60% of the community favored building a health center in their neighborhood.

Also, 14 citizens are chosen.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 14 citizens

r = number of success = exactly 5

p = probability of success which in our question is % of the community

favored building a health center in their neighborhood, i.e; 60%

LET X = Number of citizens who favored building of the health center.

So, it means X ~ $Binom(n=14, p=0.60)$

Now, Probability that exactly 5 of them favor the building of the health center is given by = P(X = 5)

P(X = 5) = $\binom{14}{5} \times 0.60^{5} \times (1-0.60)^{14-5}$

= $2002 \times 0.60^{5} \times 0.40^{9}$

= 0.0408

Therefore, Probability that exactly 5 of them favor the building of the health center is 0.0408.

4 0

3 years ago

Plzz help me Solve -24 = 6x. Show your work.

ZanzabumX [31]

Answer:

x = -4

Step-by-step explanation:

-24 = 6x

________

Switch sides:

6x = -24

________

Divide both sides by 6:

6x/6 = -24/6

________

Simplify:

X = -4

3 0

3 years ago

PLEASE ANSWER ASAP!!

SCORPION-xisa [38]

Answer:Graph A

Step-by-step explanation: -3 is your y intercept and your slope is up 2 over 1.

5 0

3 years ago

the functuon y=30+5x represents the cost y (in dollars) of having your dog groomed and buying x extra services. does this situat

Sveta_85 [38]

We want to see if the given function represents a linear function.

We will see that yes, it does.

So we have the function:

y = f(x) = 30 + 5*x

And a general linear function is written as:

y = a*x + b

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

Comparing these two, we can see that both have the same general shape, thus, our function is also a linear function.

A graph of our function also can be seen below, where it is evident that it is a line.

If you want to learn more, you can read:

brainly.com/question/20286983

8 0

3 years ago

A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence

Varvara68 [4.7K]

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

$n = 30$ -- sample size

$\bar x = 50$ -- sample mean

$\sigma = 10$ --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {30}}$

$\sigma_x = \frac{10}{5.478}$

$\sigma_x = 1.825$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.825$

$E = 3.577$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 3.577$

$Lower = 46.423$

$Lower = 46.4$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 3.577$

$Upper = 53.577$

$Upper = 53.6$ --- approximated

So, the 95% confidence interval is (46.4, 53.6)

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {90}}$

$\sigma_x = \frac{10}{9.49}$

$\sigma_x = 1.054$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.054$

$E = 2.06584$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 2.06584$

$Lower = 47.93416$

$Lower = 47.9$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 2.06584$

$Upper = 52.06584$

$Upper = 52.1$ --- approximated

So, the 95% confidence interval is (47.9, 52.1)

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

$n = 30$ $E = 3.577$

In (b), we have:

$n = 90$ $E = 2.06584$

Notice that the margin of error decreases when the sample size increases.

4 0

3 years ago