Math

QuestionFind the best grading parameters for a score of X=65X=65:
1. μ=60\mu=60, σ=5\sigma=5
2. μ=60\mu=60, σ=10\sigma=10
3. μ=70\mu=70, σ=5\sigma=5
4. μ=70\mu=70, σ=10\sigma=10

Studdy Solution

STEP 1

Assumptions1. The score on the exam is X=65X=65 . The mean (μ\mu) and standard deviation (σ\sigma) are parameters of a normal distribution3. A higher grade corresponds to a score that is more standard deviations above the mean4. The options for μ\mu and σ\sigma are μ=60,σ=5\mu=60, \sigma=5; μ=60,σ=10\mu=60, \sigma=10; μ=70,σ=5\mu=70, \sigma=5; and μ=70,σ=10\mu=70, \sigma=10

STEP 2

We need to calculate the z-score for each set of parameters. The z-score is a measure of how many standard deviations an element is from the mean. It is calculated as followsZ=XμσZ = \frac{X - \mu}{\sigma}

STEP 3

Calculate the z-score for the first set of parameters μ=60,σ=5\mu=60, \sigma=5.
Z1=65605Z1 = \frac{65 -60}{5}

STEP 4

Calculate the z-score.
Z1=6560=1Z1 = \frac{65 -60}{} =1

STEP 5

Calculate the z-score for the second set of parameters μ=60,σ=10\mu=60, \sigma=10.
Z2=656010Z2 = \frac{65 -60}{10}

STEP 6

Calculate the z-score.
Z2=656010=0.5Z2 = \frac{65 -60}{10} =0.5

STEP 7

Calculate the z-score for the third set of parameters μ=70,σ=5\mu=70, \sigma=5.
Z3=65705Z3 = \frac{65 -70}{5}

STEP 8

Calculate the z-score.
Z3=65705=1Z3 = \frac{65 -70}{5} = -1

STEP 9

Calculate the z-score for the fourth set of parameters μ=70,σ=\mu=70, \sigma=.
Z4=6570Z4 = \frac{65 -70}{}

STEP 10

Calculate the z-score.
Z4=657010=0.5Z4 = \frac{65 -70}{10} = -0.5

STEP 11

Now that we have calculated the z-scores for each set of parameters, we can determine which set gives the best grade. The best grade corresponds to the highest z-score.
The z-scores are Z=Z=, Z=0.5Z=0.5, Z3=Z3=-, and Z4=0.5Z4=-0.5. Therefore, the set of parameters that gives the best grade is μ=60,σ=5\mu=60, \sigma=5.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord