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EastWind [94]
3 years ago
15

Suppose SAT Writing scores are normally distributed with a mean of 488488 and a standard deviation of 111111. A university plans

to award scholarships to students whose scores are in the top 8%8%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.
Mathematics
1 answer:
makvit [3.9K]3 years ago
4 0

Answer:

The minimum score required for the scholarship is 644.

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 = 488, \sigma = 111

What is the minimum score required for the scholarship?

Top 8%, which means that the minimum score is the 100-8 = 92th percentile, which is X when Z has a pvalue of 0.92. So it is X when Z = 1.405.

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

1.405 = \frac{X - 488}{111}

X - 488 = 1.405*111

X = 644

The minimum score required for the scholarship is 644.

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Step-by-step explanation:

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He pays $155.25 each payment!

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alexandr402 [8]

Answer:

i)The correct option is  D.) 99.74%

ii) The correct option is B.) 68.26%

Step-by-step explanation:

i) P(10≤X≤70) = P(  (10−40)/10  ≤Z≤   (70−40 )/10 ) =  Pr(−3≤Z≤3)

= 0.9987 - 0.0013 = 0.99734

Therefore the percentage of Jen's monthly phone bills are between $40 and $100 is D.) 99.74%

ii)P(2.1≤X≤3.1) = P(  (2.1 − 2.6) /0.5   ≤ Z  ≤ (3.1−2.6 )/0.5)  =  Pr(−1  ≤Z  ≤1) )

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Therefore the percentage of students at college have a GPA between 2.1 a,d 3.1 is B.) 68.26%

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3 years ago
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Answer:

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Step-by-step explanation:

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We will use double derivative test to find maximum profit.

Differentiating P(x) with respect to x and equating to zero, we get,

\displaystyle\frac{d(P(x))}{dx} = 6400 - 36x - x^2

Equating it to zero we get,

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We use the quadratic formula to find the values of x:

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Hence, maxima occurs at x = 64.

Therefore, maximum profits are earned when x = 64 that is when 64 units are sold.

Maximum Profit = P(64) = 2,08,490.666667$

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