1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Neko [114]
3 years ago
9

A math professor notices that scores from a recent exam are normally distributed with a mean of 61 and a standard deviation of 8

. Answer the following questions using integer values.
(a) What score do 25% of the students exam scores fall below?
And, the professor decides to grade on a curve. If he wants .15% of the students to get an A, what is the minimum score required.
I have tried a "calculator" I found online and the answers it provided gave me 50% credit and I don't know which answer is correct as I don't know how to do the actual calculation.
I would appreciate referral to any valid resources as it has been many, many years since I took a math class.
(b) Suppose the professor decides to grade on a curve. If the professor wants 0.15% of the students to get an A, what is the minimum score for an A?
Mathematics
1 answer:
Alexeev081 [22]3 years ago
8 0

Answer:

a) 25% of the students exam scores fall below 55.6.

b) The minimum score for an A is 84.68.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set 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. 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 61 and a standard deviation of 8.

This means that \mu = 61, \sigma = 8

(a) What score do 25% of the students exam scores fall below?

Below the 25th percentile, which is X when Z has a p-value of 0.25, that is, X when Z = -0.675.

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

-0.675 = \frac{X - 61}{8}

X - 61 = -0.675*8

X = 55.6

25% of the students exam scores fall below 55.6.

(b) Suppose the professor decides to grade on a curve. If the professor wants 0.15% of the students to get an A, what is the minimum score for an A?

This is the 100 - 0.15 = 99.85th percentile, which is X when Z has a p-value of 0.9985. So X when Z = 2.96.

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

2.96 = \frac{X - 61}{8}

X - 61 = 2.96*8

X = 84.68

The minimum score for an A is 84.68.

You might be interested in
Lowest common factor of 72 and 108​
melamori03 [73]

Answer:

The lowest common factor of 72 and 108 is 216

5 0
3 years ago
What is the missing value in the table below?
iVinArrow [24]

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The missing value in the table below is 343. The correct option is A.

<h3>What is geometrical series?</h3>

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.

The given table if closely observed forms a geometric progression, this is because the value of the dependent variable, y is increasing by a common ratio. The common ratio in the table is,

Common ratio = y₂/y₁ = 1/(1/7) = 7

Now, for any geometric progression, the value of the nth term is given as,

Tₙ = a₁ (r)⁽ⁿ⁻¹⁾

where a₁ is the first term of the geometric progression and r is the common ratio. Therefore, the nth term of the series is,

T = a₁ (r)⁽ⁿ⁻¹⁾

Tₙ = (1/7) (7)⁽ⁿ⁻¹⁾

y = (1/7)(7)⁽ˣ⁻¹⁾

Now, the value of the y when the value of x is 5 is,

y = (1/7)(7)⁽ˣ⁻¹⁾

y = (1/7)(7)⁽⁵⁻¹⁾

y = (1/7)(7)⁴

y = (1/7) × 2401

y = 343

Hence, the missing value in the table below is 343.

Learn more about Geometrical Series here:

brainly.com/question/4617980

#SPJ1

8 0
2 years ago
The product of a number and 11 is 2
rodikova [14]
The answer should come up to n+11=2.
7 0
3 years ago
6th grade math help me plzzzzz
Pepsi [2]

Answer: -1

3 + (-4) = -1

7 0
3 years ago
Help! please it is almost due
sesenic [268]

Answer:

H and F both intersect through M. its called the (mid point) or the zero ground of the shape. Its the exact middle meaning the lines go cross but it passes by the other line, that pass by is the middle..

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Q7 Q26.) Find the quotient of the complex numbers and leave your answer in polar form.
    9·2 answers
  • A) 90°<br><br> B) 180°<br><br> C). 6°<br><br> D). 86°
    9·2 answers
  • Please tell me how to solve this, but don’t give me the answer, i want to try by myself
    5·1 answer
  • Two SUVs head toward each other from opposite ends of a freeway 460 kilometers long. If the speed of the first SUV is 49 kilomet
    9·1 answer
  • ABC and ∆PQR are similar. ∆ABC is dilated by a scale factor of 1.25 and rotated 45° counterclockwise about point B to form ∆PQR.
    7·1 answer
  • Identify the zero of the function by factoring<br> 12x²-3x=0
    15·2 answers
  • Assume you have a car worth $3,700 and investments worth another $5,400. If you owe
    6·1 answer
  • What is 3 minus (-7) with an explanation? Please do not waste my time answering randomly
    9·1 answer
  • What effect does inflation have on the prices of goods and services?
    5·2 answers
  • I need help with this question
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!