Question

Mr. Dennis gave his class a 202020-question multiple choice quiz. The distribution of raw scores had a mean of 151515 and a standard deviation of 2.52.52, point, 5. Mr. Dennis is going to multiply each raw score by 555 so the quiz is worth a total of 100100100 points. If each score is multiplied by 555, what will be the mean and standard deviation of the distribution of new scores

Answer 1

Answer:

75,62.5

Step-by-step explanation:

Given that Mr. Dennis gave his class a 20-question multiple choice quiz. The distribution of raw scores had a mean of 15 and a standard deviation of 2.5

If X is the correct questions in the 20 mcq then

X is  with mean = 15 and std dev = 2.5

when score is multiplied by 5

random variable now is

Y = 5x

E(Y) = Mean of Y = $5*E(x) = 75$

$Var(Y) = Var(5x) = 25 var(x) = 25(2.5^2)\\Std dev (Y) = 25 (2.5) = 62.5$

Thus new score out of 100 would have mean = 75 and std deviation = 62.5