Mathematics, 03.02.2020 04:04 fatlenny

The scores received by students completing a geology exam are normally distributed. if the average score is 122 and the standard deviation is 35, what percentage of students scored between 52 and 122?

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Answer from: Fauxfox

The percentage of students who scored between 52 and 122 is 47.73%

Given that :

Mean score, μ = 122

Standard deviation, σ = 35

The percentage of student who scored between 52 and 122 can be defined as :

P(z < Z) - P(z < Z)

Where, Z = (x - μ) / σ

Therefore, percentage of student who scored between 52 and 122 equals :

For x = 52 ;

P(z < Z) = P[z < (52 - 122) / 35)] = P[z < - 2]

For x = 122 ;

P(z < Z) = P[z < (122 - 122) / 35)] = P[z < 0]

Hence ;

P(z < 0) - P(z < - 2)

Using the normal distribution table or P value calculators ;

P(z < 0) = 0.5

P(z < - 2) = 0.02275

Therefore ;

P(z < 0) - P(z < - 2) = [0.5 - 0.02275] = 0.47725

The percentage of students who scored between 52 and 122 is (0.47725 × 100%) = 47.725% = 47.73%

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Answer from: Itsjazzyyy001

Notice that $52=122-70=122-2\times35$ , so the probability is equivalent to

$\mathbb P(-2$

where

follows the standard normal distribution. This is half the proportion of the students that fall within two standard deviations of the mean:

$\mathbb P(-2$

Recall the empirical rule, which states that approximately 95% of a normal distribution falls within two standard deviations of the mean. This means that

$\mathbb P(-2$

of students scored between 52 and 122.

Answer from: Quest

b mark me branliest thx

step-by-step explanation:

Answer from: Quest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

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