Final answer:
The mean points earned is 3.6 and the standard deviation is approximately 0.99 points.
Step-by-step explanation:
To find the mean of the points earned, we need to first calculate the total points earned by all the students. Since each student who passes gets 4 points, we can multiply the number of passing students (90) by 4 to get the total points earned by passing students: 90 * 4 = 360 points. The remaining 10 students who failed each get 0 points, so the total points earned by failing students is 10 * 0 = 0. Therefore, the total points earned by all the students is 360 + 0 = 360 points.
To find the mean, we divide the total points earned by the number of students: 360 / 100 = 3.6 points. So, the mean points earned is 3.6.
To calculate the standard deviation, we can use the formula for standard deviation in a sample:
Standard Deviation = sqrt( ( (passing students - mean) * (passing students - mean) + (failing students - mean) * (failing students - mean) ) / total students )
Here, passing students = 90, failing students = 10, mean = 3.6, and total students = 100.
Standard Deviation = sqrt( ( (90 - 3.6) * (90 - 3.6) + (10 - 3.6) * (10 - 3.6) ) / 100 )
Simplifying this expression, we get Standard Deviation ≈ sqrt( (81 + 37.24) / 100 ) ≈ sqrt(0.9824)
Therefore, the standard deviation (to 1 decimal place) is approximately 0.99 points.