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Serjik [45]
4 years ago
9

Scores on the Common final exam in Stat 1222 course are randomly distributed with mean 75 and Standard deviation 5. The departme

nt decides to give A to all students whose scores are in the top 10% on this exam.
What is the minimum score for a student to receive A?
Mathematics
1 answer:
SSSSS [86.1K]4 years ago
4 0

Answer:

The minimum score for a student to receive A is 81.4.

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 = 75, \sigma = 5

The department decides to give A to all students whose scores are in the top 10% on this exam.

What is the minimum score for a student to receive A?

The minimum score is the value of X when Z has a pvalue of 1-0.1 = 0.9. So it is X when Z = 1.28.

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

1.28 = \frac{X - 75}{5}

X - 75 = 1.28*5

X = 81.4

The minimum score for a student to receive A is 81.4.

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Step-by-step explanation:

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creativ13 [48]
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A Crayon is shown here.
Aleks04 [339]

The volume of the single crayon is 89.5 cm³, then the total volume of the crayons will be 2148 cm³. Then the correct option is D.

<h3>What is Geometry?</h3>

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A Crayon is shown here.

There are 24 crayons in a box.

The approximate total volume of the crayons will be

Total Volume of crayons = 24 × volume of the single crayon

The crayon is the combination of the cone and the cylinder

Then the volume of the single crayon (V₁) will be

\rm V_1 = \left ( \dfrac{1}{3} \times \pi \times r^2 \times h  \right ) + \left (  \pi \times r^2 \times h  \right )\\\\\rm V_1 = \left ( \dfrac{1}{3} \times \pi \times 1.5^2 \times 2  \right ) + \left (  \pi \times 1.5^2 \times 12  \right )\\\\V_1 = 4.712 + 84.82\\\\V_1 = 89.535 \approx 89.5

Then the Total volume will be

Total volume = 24 × 89.5

Total volume = 2148 cm³

More about the geometry link is given below.

brainly.com/question/7558603

#SPJ1

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