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zalisa [80]
3 years ago
7

Suppose a normally distributed set of data with 7800 observations has a mean of 188 and a standard deviation of 18. Use the 68-9

5-99.7 Rule to determine the number of observations in the data set expected to be below a value of 242. Round your result to the nearest single observation.
Mathematics
1 answer:
kompoz [17]3 years ago
4 0

Answer:

7788 observations are expected to be below a value of 242.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 188, standard deviation = 18

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

Percentage of observations below 242:

242 = 188 + 3*18

So 242 is three standard deviations above the mean

Of the measures below the mean, all are below 242.

Of the measures above the mean, 99.7% are between the mean of 188 and three standard deviations above the mean(242). So the percentage is:

[tex}P = 0.5 + 0.997*0.5 = 0.9985[/tex]

Number of observations below 242:

99.85% of 7800 observations

0.9985*7800 = 7788

7788 observations are expected to be below a value of 242.

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bixtya [17]

Answer:

To do this, subtract 6 from both sides. − 3_x_ + 6 − 6 > 12 − 6. −3_x_ > 6. Now divide both sides of the inequality by −3. Since you're dividing by a negative number, you need to flip the inequality sign.

Step-by-step explanation:

4 0
2 years ago
Four friends ordered a pizza cut into eight slices. The whole pizza was eaten, with each friend eating a different number of sli
raketka [301]

Answer:

{0,1,3,4}

Step-by-step explanation:

Given, total no of slices=8.

Total no of friends=4.

also each friend didnt ate more than the other three.

let a,b,c,d be no of slices ate by the friends 1,2,3,4 respectively.

given sum of a+b+c+d=8.

now applying the second condition

a\leq b+c+d \\b\leq c+d+a\\c\leq a+b+d\\d\leq a+b+c

so each of a,b,c,d must be less than or equal to 4.

which means 5 values are possible{0,1,2,3,4}.from this set you have to select 4 values such that their sum is 8.hence, those values are {0,1,3,4}.

7 0
3 years ago
Read 2 more answers
Samantha has $48 to spend on used video games. Single player games cost $6 each and multi player games cost $12 each. What equat
storchak [24]

Answer:

The equation is

6x + 12y = 48

Step-by-step explanation:

Standard form another way of writing a linear equation. It is in the form

Ax + By = C

Total amount with Samantha = $48

Single player games = $6 each

Multi player games = $12 each

Let

Number of Single player games = x

Number of Multi player games = y

The number of single player games (x) and the number of multi player games (y) Samantha can buy is

6x + 12y = 48

That is price × quantity of single player games + price × quantity of multi player games = Total amount with Samantha

3 0
3 years ago
If all city buses carry the same number of passengers, what is the least number of buses needed to carry 710 passengers? 5 10 11
noname [10]

The least number of buses needed to carry 710 passengers is 5.

Option A)5 is the correct answer.

<h3>What is the least number of buses needed to carry 710 passengers? </h3>

Given that;

  • Number of passengers n = 710
  • Least number of buses need B = ?

To get the least number of buses, we say;

Number of buses B = 710 ÷ 150

Number of buses B = 4.7 ≈ 5

The least number of buses needed to carry 710 passengers is 5.

Option A)5 is the correct answer.

Learn to solve more word problems here: brainly.com/question/2610134

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5 0
2 years ago
Help help help help pls
Monica [59]

Answer:

\theta = 82.2^\circ

Step-by-step explanation:

Let \  \angle BAC = \theta

Opposite = BC ,

Adjacent = AB = x = 3 ,

Hypotenuse = AC = y = 22

<em><u>Using trigonometric ratios.</u></em>

sin \theta = \frac{opposite}{hypotenuse }\\\\cos \theta = \frac{adjacent}{hypotenuse}\\\\tan \theta = \frac{opposite}{adjacent}

Since we have adjacent and hypotenuse we use cosine's  ratio

to find the angle.

           cos \theta = \frac{x}{y} = \frac{3}{22} \\\\\theta = cos^{-1} \frac{3}{22} = 82.16 = 82.2^\circ

6 0
3 years ago
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