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3 years ago

8

Students at XYZ Senior High School took a practice SAT. Their scores were normally distributed with a mean score of μ = 675 and

a standard deviation of σ = 25 . If 250 students took the test, how many of them scored 700 or better?
A. 200
B. 210
C. 238
D. 170

1 answer:

aleksklad [387]3 years ago

8 0

Answer:

210

Explanation:

with the 68-90-99.7 rule about 84% of students would get a 700 or better because its one std dev away from the mean so 50+34=84%

.84*250=210

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Sampling distribution involves the proportions of a data element in a given sample.

<em>The proportion of Good TV set is 0.67</em>
<em>The number of ways of selecting 5 from 6 TV sets is 6</em>
<em>The number of ways of selecting 4 from 6 TV sets is 15</em>

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Given

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From the sample space, we have:

$Good = 4$

So, the proportion (p) that are good are:

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$p = \frac{4}{6}$

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This is calculated using:

$^nC_r = \frac{n!}{(n - r)!r!}$

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So, we have:

$^6C_5 = \frac{6!}{(6 - 5)!5!}$

$^6C_5 = \frac{6!}{1!5!}$

$^6C_5 = \frac{6 \times 5!}{1 \times 5!}$

$^6C_5 = \frac{6}{1}$

$^6C_5 = 6$

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This is calculated using:

$^nC_r = \frac{n!}{(n - r)!r!}$

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So, we have:

$^6C_4 = \frac{6!}{(6 - 4)!4!}$

$^6C_4 = \frac{6!}{2!4!}$

$^6C_4 = \frac{6 \times 5 \times 4}{2 \times 1 \times 4!}$

$^6C_4 = \frac{30}{2}$

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So, the table is as follows:

$\left[\begin{array}{ccc}TV&Good&Proportion\\1,2,3,4&2&0.5&2,3,4,5&2&0.5&3,4,5,6&2&0.5\\4,5,6,1&3&0.75&5,6,1,2&4&1&6,1,2,3&3&0.75\\1,2,3,5&3&0.75&3,5,6,2&3&0.75&1,3,4,5&2&0.5\\1,3,4,6&2&0.5&1,4,5,2&3&0.75&2,4,6,1&3&0.75\\2,4,6,3&2&0.5&2,4,6,5&3&0.75&3,5,6,1&3&0.75\end{array}\right]$

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$p = \frac{Good}{n}$

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$p = 0.67$ --- proportion of Good TV

The sampling error is calculated as follows:

$SE_n = |p - p_n|$

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$\left[\begin{array}{ccc}TV&Good&SE\\1,2,3,4&2&0.17&2,3,4,5&2&0.17&3,4,5,6&2&0.17\\4,5,6,1&3&0.08&5,6,1,2&4&0.33&6,1,2,3&3&0.08\\1,2,3,5&3&0.08&3,5,6,2&3&0.08&1,3,4,5&2&0.17\\1,3,4,6&2&0.17&1,4,5,2&3&0.08&2,4,6,1&3&0.08\\2,4,6,3&2&0.17&2,4,6,5&3&0.08&3,5,6,1&3&0.08\end{array}\right]$

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<h3>What is a normative statement?</h3>

A normative statement explains what should be base of the subject according to the belief through valued judgement which shows the fairness of the subject on public policy. It generally implies relating to an evaluative standard.

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