Score on a certain nationwide college entrance examination follow a normal distribution with a mean of 500and a standard deviation of 100
so now you can use the Z table to answer questions about it.
To find the probability of scoring above a certain score on the college entrance examination, you can use the standard normal distribution and z-scores. First, let's calculate the z-score for the score you are interested in.
The formula for calculating the z-score is:
z = (x - μ) / σ
where:
z is the z-score,
x is the specific score,
μ is the mean of the distribution, and
σ is the standard deviation of the distribution.
Let's say you want to find the probability of scoring above 600 on the exam. The z-score for 600 would be:
z = (600 - 500) / 100
z = 1
Next, you can use a z-table or a calculator to find the corresponding probability. The z-table gives you the area under the standard normal distribution curve to the left of a certain z-score.
Looking up the z-score of 1 in the z-table, you can find that the probability is 0.8413. However, we need to find the probability of scoring above 600, so we subtract this probability (0.8413) from 1 (since the total area under the curve is 1):
1 - 0.8413 = 0.1587
Therefore, the probability of scoring above 600 on the college entrance examination is approximately 0.1587 or 15.87%.
You can use the same process to find the probability of scoring above any other specific score on the exam by calculating the corresponding z-score and then referring to the z-table.
To find the probability of a certain score on the nationwide college entrance examination, which follows a normal distribution with a mean of 500 and a standard deviation of 100, you can use the standard normal distribution.
The first step is to standardize the score by converting it into a z-score. The z-score formula is:
z = (x - μ) / σ
where:
- x is the score you want to find the probability for,
- μ is the mean of the distribution (500), and
- σ is the standard deviation of the distribution (100).
Once you have the z-score, you can use a standard normal distribution table or a statistical calculator to find the probability associated with that z-score.
For example, let's say you want to find the probability of getting a score of 600 on the exam. First, calculate the z-score:
z = (600 - 500) / 100 = 1
Now, you can refer to a standard normal distribution table or use a statistical calculator to find the probability associated with a z-score of 1. The table will give you the probability of the z-score falling below a certain value. In this case, you are interested in the probability of the z-score being less than 1.
Alternatively, you can use a statistical calculator or software to calculate the probability directly. Most calculators or software provide the option to input the mean, standard deviation, and z-score to find the probability.
Remember that the probability will be in decimal form, such as 0.8413, so you may need to convert it to a percentage for better understanding. In this example, the probability is approximately 84.13%, meaning there is an 84.13% chance of getting a score of 600 or lower on the exam.