OPMT 1130 Myra Andrews, Judy Li Business Statistics Winter 2018Pg 1 of 6 Lectures 9 and 10: Z-scores, Empirical Rule, Normal Distribution Z-scores Ex 1:Your final grade was 85 in Business Math and 80 in Accounting. The means and population standard deviations are below: Math Accounting Mean, μ75 60 Standard deviation, σ20 10 (a)Did you do better in Math? (b) Relative to the rest of the class did you better in Math? (c)Can Z be negative? What does it mean? (d) Can Z be zero? Sol:(a) Yes (b) No, better in accounting (c) Yes, below average (d) Yes, exactly at the average Ex 2:IQ scores for adults are bell-shaped with a mean of 100 and a standard deviation of 15. What minimum IQ do you need to qualify as an outlier on the high side? (145 or higher) ). .
OPMT 1130 Myra Andrews, Judy Li Business Statistics Winter 2018Pg 2 of 6 1.The grades in a first-year Economics course are normally distributed with a mean of 60% and a standard deviation of 10%. Students need to get 50% to pass the course. (a)What percentage of students failed the course? (b)You got 70% in the course. What percentage of students did better than you? You did better than what percentage of students? (c)What percentage of students got between (i) 70% and 80%? (ii) 50% and 70%? (d)What percentage of students got a below average grade but still passed the course? (e)What percentage of students got a grade of 99% or higher? (f)What percentage of students got a grade between 60% and 99%? (g)If 121 students got a grade of 67% or higher, how many students took the course? (h)90% of students got a grade below what value? (i)The grades of the middle 90% of students are between what two values? (j)What is the minimum grade needed to be in the top 5% of students? (k)2 out of every 3 students got a grade higher than what value? 2.A cereal maker has a machine that fills the cereal boxes.