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
How do write 2/100000 as a decimal
ahrayia [7]
0.00005 is the answer.
6 0
3 years ago
Read 2 more answers
A área do círculo mede 196 π cm². Qual a medida do seu raio?
AleksandrR [38]

Hey there!!

  • The area of a circle = πr²

The area is given as 196π

Hence,

196π = πr²

... r²= 196

... r = √196

... r = 14

<em>Hence, the radius is 14 cm. </em>

<em>Hope it helps!</em>

8 0
3 years ago
Read 2 more answers
Explian how you can find the number of feet in 20 yards
natka813 [3]
1 yard is = to 3 feet.
20 yards = to 20 X 3 feet
your answer is 60 feet
3 0
3 years ago
Read 2 more answers
A box contains 17 balls numbered 1 through 17. Two balls are drawn in succession without replacement. If the second ball has the
Brilliant_brown [7]

Answer:

1 ; 7 /17

Step-by-step explanation:

17 balls numbered 1 through 17

Picking without replacement :

If the second ball picked = 4

P(first ball has a smaller number)

Numbers less Than = (3, 2, 1)

P(number less than second ball Given 4 is drawn for second ball) :

= (3/17 * 1/16) ÷ (3/17 * 1/16) +) 14/17 * 0)

= (3 / 272) / (3 /272) * 0

= 3 / 272 * 272 / 3

= 1

2.)

(8/17 * 7/8) ÷ (8/17 * 7/8) + (9/17 * 1/17)

7/17 ÷ (7 /17) + 10/17

7 /17 ÷ 17/17

7/17 ÷ 1

7 /17

7 0
3 years ago
Plz, answer the question in the photo.
kotegsom [21]

Answer:

H

Step-by-step explanation:

Step 1 of 2: Subtract, sub-step b: Convert mixed number to improper fraction.

Convert mixed number to improper fraction

2 and 1 over 32

1

3

= ( 2 × 3 ) over 3

2 × 3

3

+ 1 over 3

1

3

= ( 6 + 1 ) over 3

6 + 1

3

= 7 over 3

7

3

Step 1 of 2: Subtract, sub-step c: Find common denominator.

Find common denominator

32 over 9

32

9

− 7 over 3

7

3

= ( 32 × 1 ) over ( 9 × 1 )

32 × 1

9 × 1

− ( 7 × 3 ) over ( 3 × 3 )

7 × 3

3 × 3

= 32 over 9

32

9

− 21 over 9

21

9

9 is the least common multiple of denominators 9 and 3. Use it to convert to equivalent fractions with this common denominator.

Step 1 of 2: Subtract, sub-step d: Subtract.

Subtract

32 over 9

32

9

− 21 over 9

21

9

= ( 32 − 21 ) over 9

32 − 21

9

= 11 over 9

11

9

Step 1 of 2: Subtract.

Step 2 of 2: Simplify.

Simplify

11 over 9

11

9

= 1 and 2 over 91

2

9

4 0
3 years ago
Other questions:
  • A rectangular window is 1 meter high and 2 meters wide. What is the perimeter of the window in meters? What is it in centimeters
    10·1 answer
  • Jessica completed 21 math problems in 14 minutes. At this rate, how many math problems could she complete in 30 minutes?
    9·1 answer
  • A car is driven on a straight track such that its displacement from the starting point is given as x = t + 2t2. What is the aver
    8·1 answer
  • Brandy took 3 friends out for dinner. The cost of the meal was 46.15 she left the 20% tip what was the total cost including the
    5·1 answer
  • 15 points for free i guess lol
    14·2 answers
  • How to find the surface area of a 3D shape?
    8·1 answer
  • Rectangle A and B have the same Area. Rectangle A has a length of 7m and a width of 4m. Rectangle B has a width of 10m. What is
    11·1 answer
  • Kasey are u online plz reply me 208x492​
    5·2 answers
  • Combine like terms to create an equivalent expression. Enter coefficients as simplified proper or improper fractions or integers
    15·1 answer
  • triangle ghi is dilated to form new triangle jkl. if angle h is congruent to angle k, what other information will prove that the
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!