An observed frequency distribution of exam scores is as follows: i) Assuming a n
ID: 3222059 • Letter: A
Question
An observed frequency distribution of exam scores is as follows: i) Assuming a normal distribution with mu = 75 and sigma = 15, find the probability of a randomly selected subject belonging to each class. (Use boundaries of 59.5, 69.5, 79.5, 89.5, 100.) ii) Using the probabilities found in part (i), find the expected frequency for each category iii) Use a 0.05 significance level to test the claim that the exam scores were randomly selected from a normally distributed population with mu = 75 and sigma = 15.Explanation / Answer
i)
Below table shows the probability of randomly selected subject beloning to each class calculated as per central limit theorem
P(X<59.5) = P(z<(59.5 - 75)/15) = P(z<-1.33) = 0.1507
P(59.5<X<69.5) = P(z<(69.5 - 75)/15) - P(X<59.5) = 0.3569 - 0.1507 = 0.2062
P(69.5<X<79.5) = P(z<(79.5 - 75)/15) - P(X<69.5) = 0.6179 - 0.3569 = 0.2610
P(79.5<X<89.5) = P(z<(89.5 - 75)/15) - P(X<79.5) = 0.8331 - 0.6179 = 0.2153
P(89.5<X<100) = P(z<(100 - 75)/15) - P(X<89.5) = 0.9522 - 0.8331 = 0.1191
ii)
Below table calculates the expected frequency of students based on above calculated probabilities. Here we use the total number of 300 students to calculate the expected frequecy.
P(X<60) = 0.15072 P(60<X<69) = 0.20621 P(70<X<79) = 0.26098 P(80<X<89) = 0.21523 P(90<X<100) = 0.11906