Scores on an English test are normally distributed with a mean of 78% and a standard deviation of 4.5%. Find the value of the first quartile.
you want Z such that P(Z>z) = 0.75
That means that Z >= -.674
.674*4.5 = 3.033
So, you want a score of at least 78-3.033 = 74.967
The 1st quartile ends at a score of 75%
You can play around with Z table stuff at
http://davidmlane.com/hyperstat/z_table.html
Thank you so much!!!
To find the value of the first quartile, you need to perform the following steps:
Step 1: Convert the mean and standard deviation to decimals. The mean is 78% which is 0.78, and the standard deviation is 4.5% which is 0.045.
Step 2: Calculate the z-score for the first quartile. The first quartile corresponds to the 25th percentile, which has a z-score of -0.674. You can find this value by looking it up in a standard normal distribution table or using a calculator.
Step 3: Use the formula for z-score to find the raw score value. The formula is: raw score = (z-score * standard deviation) + mean.
In this case, the raw score for the first quartile would be:
raw score = (-0.674 * 0.045) + 0.78
Step 4: Calculate the value of the first quartile by converting the raw score back to a percentage. Multiply the raw score by 100 to convert it to a percentage.
In this case, the value of the first quartile would be:
value of first quartile = (raw score * 100)%
value of first quartile = ((-0.674 * 0.045) + 0.78) * 100
To summarize, the value of the first quartile for the English test scores is ((-0.674 * 0.045) + 0.78) * 100.