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taurus [48]
1 year ago
7

What is the probability that a random sample of 10 second grade students from the city results in a mean reading rate of more th

an 96 words per​ minute
Mathematics
1 answer:
Vinvika [58]1 year ago
3 0

Using the normal distribution, it is found that there is a 0.1029 = 10.29% probability that the sample mean is above 96.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

Researching the problem on the internet, the parameters are given as follows:

\mu = 92, \sigma = 10, n = 10, s = \frac{10}{\sqrt{10}} = 3.1623

The probability that the sample mean is above 96 is <u>one subtracted by the p-value of Z when X = 96</u>, hence:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem:

Z = \frac{X - \mu}{s}

Z = \frac{96 - 92}{3.1623}

Z = 1.265

Z = 1.265 has a p-value of 0.8971.

1 - 0.8971 = 0.1029 = 10.29% probability that the sample mean is above 96.

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

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A triangle has 2 sides that equal 5 inches. The other side equals 4 inches
miskamm [114]

Answer:

Isosceles triangle

Step-by-step explanation:

It is assumed that the triangle is a right angle triangle, implying that Pythagoras theorem becomes applicable.

If the first side is represented by x and the second side by y,

x + y = 5

The hypotenuse is always the longest side hence it can be presumed to be 4 since both x and y cannot be more than 5.

Therefore using pythagoras equation:

hyp^2 = sqrt(opp^2 + adj^2)

this implies that

4^{2} = \sqrt{x} (x^{2} +y^{2}

therefore

16 = sqrt (x^2 + y^2) ----------------- (i)

since x + y = 5, y = 5 - x ------------------- (ii)

substituting (ii) into eqn (i)

16 = sqrt ( x^2 + (5-X)^2)

16 = sqrt( x^2 + 25 -10x + x^2)

16 = sqrt( x^2 + x^2 - 10x + 25)

16 = sqrt( 2x^2 - 10x + 25)

squaring both sides

256 = 2x^2 - 10x + 25

this can be refined as

2x^2 - 10x - 231 = 0

Solving using quadratic equation:

where a = 2, b = -10 and c = -231

x = 13.53  or -8.53.

Since x is a side of a triangle that cannot be negative,

x = 13.53 but x can never be greater than 5 since x + y = 5

This implies that the triangle is not a right angle triangle; it is most likely an  isosceles triangle with two sides of equal length such that x = y = 2.5 inches while the longest side; the hypotenuse is 4 inches.

substituting for x in

4 0
3 years ago
Solve the inequality. q - 1 1/3 &gt; -2 1/2
ioda

\Leftrightarrow q>1\frac{1}{6}

Step-by-step explanation:

  q-\frac {11}{3}>-2\frac{1}{2}

\Leftrightarrow q>-2\frac{1}{2}+\frac {11}{3}

\Leftrightarrow q>\frac{7}{6}

\Leftrightarrow q>1\frac{1}{6}

6 0
2 years ago
an art teacher has 28 students in her first period class and 24 in her second period class if almost 30 of the students in these
tatiyna

Answer:

im not sure if this answer is correct but i think its 22

6 0
2 years ago
Read 2 more answers
Please help I will mark you brainliest​
ddd [48]
Kbivivivogxoyxoycoycoycoycoycoycoycoyco
8 0
3 years ago
What is the simplified form of <br><br> (X/3-y/4)/(x/4+y/3) ? (6 points)
Fofino [41]

Option 2: \frac{4x-3y}{3x+4y} is the right answer

Step-by-step explanation:

Given fraction is:

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

To solve the fraction, Taking LCM in denominator and numerator

=\frac{\frac{4x-3y}{12} }{\frac{3x+4y}{12}}

When the numerator and denominator both have fractions, the simplified form is obtained be multiplying the numerator with reciprocal of the denominator. So,

= \frac{4x-3y}{12} * \frac{12}{3x+4y}\\=\frac{4x-3y}{3x+4y}

Hence,

Option 2: \frac{4x-3y}{3x+4y} is the right answer

Keywords: fractions, simplification

Learn more about fractions at:

  • brainly.com/question/4401748
  • brainly.com/question/4459688

#LearnwithBrainly

4 0
3 years ago
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