High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ The scores received by students completing a geology exam are normally distributed. If the average score is 122 and the standard deviation is 35, what percentage of students scored between 52 and 122?

Answer :

The percentage of students who scored between 52 and 122 is 47.73%

Given that :

Mean score, μ = 122

Standard deviation, σ = 35

The percentage of student who scored between 52 and 122 can be defined as :

P(z < Z) - P(z < Z)

Where, Z = (x - μ) / σ

Therefore, percentage of student who scored between 52 and 122 equals :

For x = 52 ;

P(z < Z) = P[z < (52 - 122) / 35)] = P[z < - 2]

For x = 122 ;

P(z < Z) = P[z < (122 - 122) / 35)] = P[z < 0]

Hence ;

P(z < 0) - P(z < - 2)

Using the normal distribution table or P value calculators ;

P(z < 0) = 0.5

P(z < - 2) = 0.02275

Therefore ;

P(z < 0) - P(z < - 2) = [0.5 - 0.02275] = 0.47725

The percentage of students who scored between 52 and 122 is (0.47725 × 100%) = 47.725% = 47.73%

Learn more : https://brainly.com/question/14971859

Notice that [tex]52=122-70=122-2\times35[/tex], so the probability is equivalent to

[tex]\mathbb P(-2
where [tex]Z[/tex] follows the standard normal distribution. This is half the proportion of the students that fall within two standard deviations of the mean:

[tex]\mathbb P(-2
Recall the empirical rule, which states that approximately 95% of a normal distribution falls within two standard deviations of the mean. This means that

[tex]\mathbb P(-2
of students scored between 52 and 122.

Other Questions