a full scholarship to any student who scores in the top 4% of students on the SMRT standardized exam. SMRT scores have a mean of 260 and a standard deviation of 22. What score does a student need to attain in order to receive the scholarship?
this is how I worked it
1.00-.04=.96 which z-score would be .8315
.8315*22+260= 280 worksheet answer says 299 can some show me where I went wrong
To find the score a student needs to attain in order to receive the scholarship, you can use the concept of z-scores.
A z-score represents the number of standard deviations an individual score is from the mean. In this case, you want to find the z-score corresponding to the top 4% of students.
To start, you correctly calculated 1 - 0.04 = 0.96, which represents the area under the normal distribution curve to the left of the cutoff score.
Next, you need to find the z-score corresponding to this area under the curve. You can use a z-score table or a calculator to find this value. The z-score corresponding to an area of 0.96 is approximately 1.75.
Now, using the formula for z-score:
z = (X - mean) / standard deviation
Plug in the values you have:
1.75 = (X - 260) / 22
Now, solve for X by rearranging the equation:
X - 260 = 1.75 * 22
X - 260 = 38.5
X = 38.5 + 260
X = 298.5
So, the score a student needs to attain in order to receive the scholarship is approximately 298.5.
It seems like you made a small calculation error when multiplying 0.8315 and 22. The correct result should be 18.29, not 38.5, leading to an answer of approximately 278.29.