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Salsk061 [2.6K]
3 years ago
8

A school wishes to accept 2000 students for their freshman class, and they expect 20,000 applications. In order to make their ad

missions decisions very easy, the only criterion they will use is SAT score. So, their goal is to accept a student if and only if their SAT score is in the top 10%. However, because their computer system is so old, the applications only come in one at a time, and they must decide whether to accept or reject before moving on to the next application. Assuming that SAT scores are normally distributed with a mean of 1000 and a standard deviation of 200, how should they set the score threshold to end up with as close to 2000 students as possible? Give your answer first symbolically (in terms of a pdf, cdf, etc), then use a normal distribution table1 to provide a numerical answer.
Mathematics
1 answer:
vovangra [49]3 years ago
3 0

Answer:

456

Step-by-step explanation:

Let X be the SATscore scored by the students

Given that X is normal (1000,200)

By converting into standard normal variate we can say that

z=\frac{x-1000}{200} is N(0,1)

To find the top 10% we consider the 90th percentile for z score

Z 90th percentile = 1.28

X= 200+1.28(200)\\= 200+256\\=456

i.e. only students who scored 456 or above only should be considered.

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Answer:

x = 1

Step-by-step explanation:

If you have any questions feel free to ask in the comments

5 0
2 years ago
an outlier may be defined as a data point that is more than 1.5 times the interquartile range below the lower quartile or is mor
Ira Lisetskai [31]

Supposing a normal distribution, we find that:

The diameter of the smallest tree that is an outlier is of 16.36 inches.

--------------------------------

We suppose that tree diameters are normally distributed with <u>mean 8.8 inches and standard deviation 2.8 inches.</u>

<u />

In a normal distribution with mean \mu and standard deviation \sigma, the z-score 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, which is the percentile of X.<u> </u>

<u />

In this problem:

  • Mean of 8.8 inches, thus \mu = 8.8.
  • Standard deviation of 2.8 inches, thus \sigma = 2.8.

<u />

The interquartile range(IQR) is the difference between the 75th and the 25th percentile.

<u />

25th percentile:

  • X when Z has a p-value of 0.25, so X when Z = -0.675.

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

-0.675 = \frac{X - 8.8}{2.8}

X - 8.8 = -0.675(2.8)

X = 6.91

75th percentile:

  • X when Z has a p-value of 0.75, so X when Z = 0.675.

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

0.675 = \frac{X - 8.8}{2.8}

X - 8.8 = 0.675(2.8)

X = 10.69

The IQR is:

IQR = 10.69 - 6.91 = 3.78

What is the diameter, in inches, of the smallest tree that is an outlier?

  • The diameter is <u>1.5IQR above the 75th percentile</u>, thus:

10.69 + 1.5(3.78) = 16.36

The diameter of the smallest tree that is an outlier is of 16.36 inches.

<u />

A similar problem is given at brainly.com/question/15683591

3 0
2 years ago
Dante's Mom wants to build a fence around their yard. Here are the measurements of the yard. What are the measurements of the mi
timama [110]

Answer:

(a)The missing measurements are 9 feet and 16\frac{1}{4}$ feet.

(b)Therefore, the length of the fence is  97\frac{1}{2}$ feet

Step-by-step explanation:

The diagram of the yard is attached below.

(a)I have labeled the missing dimensions of the yard as x and y.

Therefore:

y+8\frac{1}{4}=17 \frac{1}{4}\\y=17 \frac{1}{4}-8\frac{1}{4}\\y=9$ feet

Similarly:

x+15\frac{1}{4}=31\frac{1}{2}\\x=31\frac{1}{2}-15\frac{1}{4}\\x=31-15+\frac{1}{2}-\frac{1}{4}\\x=16+\frac{1}{4}\\x=16\frac{1}{4}$ feet

The missing measurements are 9 feet and 16\frac{1}{4}$ feet.

(b)Length of the Fence

The fence is rectangular shaped with:

Length = 31\frac{1}{2}$ feet

Width = 17 \frac{1}{4}$ feet

Perimeter of a Rectangle = 2(L+W)

Therefore, the length of the fence

=2(31\frac{1}{2}+17 \frac{1}{4})\\=2(31+17+\frac{1}{2}+ \frac{1}{4})\\=2(48+ \frac{3}{4})\\=96+\frac{3}{2}\\=97\frac{1}{2}$ feet

8 0
3 years ago
Determine length of RT
dalvyx [7]

Answer:

20

Step-by-step explanation:

6 0
2 years ago
What's 51/99 in simplest form?
Serga [27]
Both the numerator and denominator can be divided by three, so the simplest form is \frac{17}{33}.
3 0
3 years ago
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