The mean NAT scores of Grade 10 students is 65. Sixty (60) students were chosen and found that the standard deviation of their score is 5. What is the probability that their mean is between 64 and 67.

Answer 1

Construct the inequality (64 − 65)/5 ≤ P ≤ (67 − 65)/5 or -0.2 ≤ P ≤ 0.4.

A Table Of Proportions Of Area Under The Standard Normal Curve

will give areas corresponding to Z = -0.2 & Z = 0.4 close to -0.0793 & 0.1554

A highly accurate calculator program will give areas corresponding

to -0.2 & 0.4 of -0.07925970944 & 0.1554217416.

The Probability that the Mean falls between 64 & 67 is

given by 0.1554217416 − -0.07925970944 or 0.234681451

equivalent to 0.235. Use of the rounded values from the Table

will give 0.1554 − -0.0793 or .2347, again equivalent to 0.235.