Question

TIMSS 2003 (Trends in International Mathematics and Science Study) focused on the mathematics and science achievement of eighth-graders throughout the world. A total of 45 countries (including the United States) participated in the study. The mean math exam score for U.S. students was 496 with a standard deviation of 93. Assume the scores are normally distributed and a sample of 154 students is taken. (Give your answers correct to four decimal places.)

(a) Find the probability that the mean TIMSS score for a randomly selected group of eigth-graders would be between 499 and 512.

(b) Find the probability that the mean TIMSS score for a randomly selected group of eighth-graders would be less than 524.

(c) Do you think the assumption of normality is reasonable? Explain. (a) Yes, since the sample size is large. (b) Yes, since the sample size is small. (c) No, since the sample size is large.

Answer 1

Let X follows N(u = 496,0 =93) a) P(499 < Ē <512)=P 499 – 496 - 1 % 154 % =P(0.40<z«2.13) 512 - 496 93,154 = P(: <2.13) - P(Z <0.40) Excel function, (= NORMSDIST(:))) = 0.9834-0.6554 = 0.3280 b) P(F=520)=PFTS P(X < 524)=P - X - u 524 - 496 V154 = P(Z <3.74) = 0.9999 (excelfunction(= NORMSDIST(-))) c) Yes, the assumption of normality is reasonable since the sample size is large Answer: option (a)