Question

Massachusetts school systems are considered to be the best in the nation; 18.2% of Massachusetts 8th graders achieved an advanced-level performance on the math portions of their national exams. This is more than twice the national rate. If a random sample of 250 8th graders was selected, what is the probability that more than 20% achieved an advanced-level performance on their math portion?

Answer 1

Given data

population proportion of sucess (p)=0.182

population proportion of failure (q)=1-p=1-0.182=0.818

Now size of the Sample taken (n)=250

Sample proportion of sucess

and we have to find the probablity of getting the smple propertion of sucess more than 20 % that is

Now lets calculate the test statistic first

So we have from the formula

Now from the standard table of probablity distribution for Z score we have the respective probablity value forr the Z=0.74 is .since it is the area under the Z=0.74 so it is the probablity of getting student less than 20% who achived the advanced level performance

so the probablity of getting student more than 20% who achived the advanced level performance

so if we round the answer up to two place than answer will be