Probability question (mean, SD)

In summary, the conversation discusses the normal distribution of scores on an examination with a mean of 58 and a standard deviation of 18. Part (a) asks for the probability of scoring higher than 72, which can be found by standardizing the value and using the $z$-score formula. Part (b) discusses the top 10% of the distribution receiving an A grade and asks for the minimum score required for an A. Part (c) mentions a fail grade for scores of 40 or below and asks for the proportion of failures in the examination. Part (d) inquires about the probability of at most 2 failures in a sample of 10 students. Finally, part (e) asks for the probability
  • #1
tiffyuyu
2
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.
 
Mathematics news on Phys.org
  • #2
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:

\(\displaystyle z=\frac{x-\mu}{\sigma}\)

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

Related to Probability question (mean, SD)

1. What is the difference between mean and standard deviation?

Mean is the average value of a set of data, calculated by adding all the values and dividing by the total number of values. Standard deviation is a measure of how spread out the data is from the mean. It measures the variability or dispersion of the data set.

2. How is probability calculated using mean and standard deviation?

Probability can be calculated by taking a value from the data set, subtracting the mean from it, and then dividing by the standard deviation. This calculation will give you a standardized score, or Z-score, which can then be used to find the probability using a normal distribution table.

3. What is the significance of mean and standard deviation in probability?

Mean and standard deviation are important because they can help us understand the distribution of data and make predictions about future events. In probability, they are used to calculate the chances of events occurring and to measure the likelihood of a certain outcome.

4. Can mean and standard deviation be used for any type of data?

Mean and standard deviation are commonly used for quantitative data, which is numerical data that can be measured. They can also be used for continuous data, which can take on any value within a certain range. However, they may not be suitable for categorical data, which is non-numerical data that is divided into categories.

5. How can mean and standard deviation be used to compare two sets of data?

Mean and standard deviation can be used to compare two sets of data by looking at the difference between their mean values and the variability of their data. If the mean values are similar and the standard deviations are small, the two data sets are likely to be similar. However, if the mean values are different and/or the standard deviations are large, the two data sets are likely to be different.

Similar threads

MHB Does the entrance test score determine the final exam score?
    • General Math
Replies
3
Views
1K
MHB Test of hypothesis involving the population mean 𝝁 when the variance is known
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
895
MHB What is the probability of exceeding maximum weight with a normal distribution?
    • General Math
Replies
2
Views
1K
MHB This is sampling distribution can you help me with this problem
    • General Math
Replies
4
Views
3K
MHB Probability - Amount of money in pocket
    • Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
MHB Winning Tennis with Probability 0.3 and 0.7
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
MHB Help with Probability, Roulette, and Population Statistics
    • General Math
Replies
3
Views
2K
MHB Could use help, know the answers but with the process and equations
    • General Math
Replies
2
Views
2K
Calculating Probability for Test Scores: Mean 2.725, SD 1.329, 61 Students
    • General Math
Replies
5
Views
2K
A Monte Carlo to compute uncertainties, why report the mean and SD?
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
800

Hot Threads

Recent Insights

Back
Top