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Wittaler [7]
1 year ago
8

Data collected over a long period of time show that the length of time x to complete a particular college entrance test is norma

lly distributed with an average of 125 minutes and a standard deviation of 18 minutes. What is the probability that a student taking this test will finish in 100 minutes or less? round your answer to 4 decimal places. Remember to round all z values to 2 decimal places.
Mathematics
1 answer:
Finger [1]1 year ago
7 0

Using the z-table, the probability that a student taking this test will finish in 100 minutes or less is 0.0824 or 8.24%.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 100

μ = mean = 125

σ = standard deviation = 18

z-score = (100 – 125) / 18

z-score = (-25) / 18

z-score = -1.39

Find the probability that corresponds to the z-score in the z-table. (see attached images)

-1.39 - (-1.3) : -1.4 - (-1.3) = x - 0.0968 : 0.0808 - 0.0968

-0.09 : -0.1 = x - 0.0968 : -0.016

x - 0.0968 = -0.09(-0.016)/-0.1

x = -0.0144 + 0.0968

x = 0.0824

x = 0.0824

Hence, the probability that a student taking this test will finish in 100 minutes or less is 0.0824 or 8.24%.

Learn more about probability here: brainly.com/question/26822684

#SPJ4

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Using the value of x and plugging said value into #1 or #2, we can find y
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OR

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3 years ago
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Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than
Fittoniya [83]
Inequation 1: 

\frac{2}{3}x-3 \geq y

to plot the pairs (x, y) for which the inequation holds, draw the line y=\frac{2}{3}x-3

then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.

we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.

inequation 2: 

y+ \frac{2}{3}x\ \textless \ 4

y\ \textless \ - \frac{2}{3} x+ 4



draw the lines 

i)  y=\frac{2}{3}x-3          use points (0, -3),  (3, -1)

ii)y=- \frac{2}{3} x+ 4       use points ( 0, 4),   (3, 2)


let's use the point P(3, 3) to see what region of the lines need to be coloured:

\frac{2}{3}x-3 \geq y  ; 
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2-3 \geq 3, not true so we color the region not containing this point


y+ \frac{2}{3}x\ \textless \ 4
(3)+ \frac{2}{3}(3)\ \textless \ 4
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The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.



4 0
3 years ago
Examine the following equation and classify the type of solution.
Viktor [21]

Answer:

<h2>infinitely many solutions</h2>

Step-by-step explanation:

5x - 6 = 3x - 6 + 2x     <em>combine like terms</em>

5x - 6 = (3x + 2x) - 6

5x - 6 = 5x - 6         <em>subtract 5x from both sides</em>

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3 years ago
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lara31 [8.8K]
The numbers given in the problem above are part of an arithmetic sequence with first and sixth terms equal to -21 and -36, respectively. Firstly, calculate for the common difference (d).
 
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The arithmetic mean is calculated by adding -3 to the term prior to it. 

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Thus the four arithmetic means are -24, -27, -30, and -33.
4 0
3 years ago
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