Probability question (mean, SD)

  • Context: MHB 
  • Thread starter Thread starter tiffyuyu
  • Start date Start date
  • Tags Tags
    Mean Probability sd
Click For Summary
SUMMARY

The discussion focuses on the application of normal distribution in statistics, specifically regarding examination scores with a mean of 58 and a standard deviation of 18. Participants analyze the probability of scoring above 72, determine the minimum score for an A grade, and assess the proportion of failures for scores of 40 or below. Key calculations involve standardizing scores using the z-score formula, \( z = \frac{x - \mu}{\sigma} \), to facilitate probability assessments.

PREREQUISITES
  • Understanding of normal distribution and its properties
  • Familiarity with z-scores and standardization techniques
  • Basic knowledge of probability calculations
  • Ability to interpret statistical results in educational contexts
NEXT STEPS
  • Learn how to calculate probabilities using the normal distribution table
  • Explore the concept of confidence intervals in statistics
  • Study the Central Limit Theorem and its implications for sample means
  • Investigate statistical software tools like R or Python for performing statistical analysis
USEFUL FOR

Students, educators, and statisticians who are involved in analyzing examination scores and understanding the implications of normal distribution in educational assessments.

tiffyuyu
Messages
2
Reaction score
0
Scores on an examination are assumed to be normally distributed with a mean of 58 and a standard deviation of 18.

(a) What is the probability that a person taking the examination scores higher than 72?

(b) Suppose that students scoring in the top 10% of this distribution are to receive an A grade. What is the minimum score a student must achieve to earn an A grade?

(c) Suppose that students scoring 40 or below are to receive a fail grade F. What is the proportion of failure in the examination?

(d) According to (c), if 10 students are randomly selected, what is the probability that there are at most 2 failures?

(e) Find the probability that the mean score of 9 randomly selected students exceeds 65.
 
Physics news on Phys.org
Hello, tiffyuyu! :D

Just for future reference, we ask that people posting questions show what they have tried so far, so that those helping have an idea where you are stuck and how best to help.

Let's begin with part a).

First. we need to standardize the raw datum given, so we need to use the following formula:

$$z=\frac{x-\mu}{\sigma}$$

Can you use this to convert the value of 72 into a $z$-score?
 

Similar threads

MHB Sampling Distribution of the Sample Means from an Infinite Population
  • · Replies 1 ·
Replies
1
Views
1K
MHB Does the entrance test score determine the final exam score?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Probability - Amount of money in pocket
  • · Replies 6 ·
Replies
6
Views
2K
MHB Winning Tennis with Probability 0.3 and 0.7
  • · Replies 4 ·
Replies
4
Views
17K
Graduate Monte Carlo to compute uncertainties, why report the mean and SD?
  • · Replies 2 ·
Replies
2
Views
1K
High School Probability of hitting a target
  • · Replies 10 ·
Replies
10
Views
3K
MHB Mean & Std Dev for Norm Dist. Exam Marks - 450 Stud.
  • · Replies 1 ·
Replies
1
Views
2K
MHB What is the probability of exceeding maximum weight with a normal distribution?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Find the 90% two-sided confidence interval for the mean score.
  • · Replies 3 ·
Replies
3
Views
2K
High School Relative And Absolute Probability (Probability Of Picking A Red Ball)
  • · Replies 8 ·
Replies
8
Views
3K