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Ira Lisetskai [31]
3 years ago
5

According to the College Board website, the scores on the math part of the SAT (SAT-M) in a recent year had a mean of 507 and st

andard deviation of 111. Assume that SAT-M scores have a normal probability distribution. One of the criteria for admission to a certain engineering school is an SAT-M score in the 98th percentile. This means the score is in the top 2% of scores. Find the actual SAT-M score marking the 98th percentile? Show your work. Interpret your result. Note: You will need the Inverse Normal Distribution Calculator below.
Mathematics
1 answer:
Leviafan [203]3 years ago
8 0

Answer:

The actual SAT-M score marking the 98th percentile is 735.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 507, \sigma = 111

Find the actual SAT-M score marking the 98th percentile

This is X when Z has a pvalue of 0.98. So it is X when Z = 2.054. So

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

2.054 = \frac{X - 507}{111}

X - 507 = 2.054*111

X = 735

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How much of a 14% iodine solution should be added to 89 ounces of a 47% iodine solution to get a 29% solution
Elza [17]
Whatever% of anything is just (whatever/100) * anything.

x = ounces of 14% iodine.

y = ounces of 29% iodine.

we know that in a 14% iodine solution, 14% is iodine and the rest is something else, we also know that "x" ounces of the solution have 14% of iodine, how much is that?  (14/100) * x, or 0.14x.

likewise, in the 89 ounces of 47% solution there is (47/100) * 89 of iodine.

and likewise as well, in "y" ounces of 29% iodine there is (29/100) * y, or 0.29y of iodine.

bearing in mind that, whatever "x" and "y" may be, x + 89 = y, and that the sum of the iodine amounts also will equate 0.29y.

\bf \begin{array}{lccclll}
&\stackrel{ounces}{amount}&\stackrel{\%~of~iodine}{quantity}&\stackrel{iodine~oz}{amount}\\
&------&------&------\\
\textit{14\% solution}&x&0.14&0.14x\\
\textit{47\% solution}&89&0.47&41.83\\
------&------&------&------\\
mixture&y&0.29&0.29y
\end{array}
\\\\\\
\begin{cases}
x+89=\boxed{y}\\
0.14x+41.83=0.29y\\
--------------\\
0.14x+41.83=0.29\left( \boxed{x+89} \right)
\end{cases}
\\\\\\
0.14x+41.83=0.29x+25.81\implies 16.02=0.15x
\\\\\\
\cfrac{16.02}{0.15}=x\implies 106.8=x
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A container of coffee is 1/6 full. That container contains 2/3 of a pound of coffee write a division expression that represents
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Let us assume total capacity of the container = x pounds.

Container contains 1/6th coffee of total x pounds,  that is x/6 pounds.

We also given that 1/6th part is equal to 2/3 of a pound.

So, we could setup an equation now.

x/6 pounds equals 2/3 of a pound.

\frac{x}{6} = \frac{2}{3}

Dividing both sides by 1/6, we get

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Division expression that represents the capacity of the container = 2/3 ÷ 1/6.


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The class scores of a history test have a normal distribution with a mean Mu = 79 and a standard deviation Sigma = 7. If Opal’s
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The value of z score for the history class test of Opal’s test score is negative one (-1).

<h3>What is normally distributed data?</h3>

Normally distributed data is the distribution of probability which is symmetric about the mean.

The mean of the data is the average value of the given data. The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

The z score for the normal distributed data can be given as,

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The mean value of the scores of history class is,

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Here, the test score of the Opal’s is 72. Thus the z score for her test score can be given as,

z=\dfrac{72-79}{7}\\z=-1

Hence, the value of z score for the history class test of Opal’s test score is negative one (-1).

Learn more about the normally distributed data here;

brainly.com/question/6587992

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