Mathematics 30 June 1999 Grade 12 Diploma Exam

38. Cases of apples delivered to a grocery store have a mean mass of 20 kg with
a standard deviation of 0.8 kg. Assuming a normal distribution, the probability of
choosing, at random, a case with a mass between 19.0 kg and 21.2 kg is
A. 0.8664
B. 0.8276
C. 0.7888
D. 0.4970
39. A teacher gave a class a physics test. The test scores were normally distributed and
had a mean of 40% with a standard deviation of 10%. Dan received a mark of
65% on his test. The teacher adjusted the mean of the test to 60% and adjusted
the standard deviation to 14%. If the teacher kept Dan’s z-score constant, then
what would Dan’s new mark be?
A. 85%
B. 93%
C. 95%
D. 98%
40. The manufacturer of “Greenline” lawnmowers gathers information on how soon
after purchase the mowers require their first repair. The data is normally
distributed with a mean of 7.5 years and a standard deviation of 2 years. If
35 000 “Greenline” mowers are sold in one year, then the number of those
“Greenline” mowers expected to require repairs in the first 5 years is
A. 3 696 mowers
B. 13 804 mowers
C. 21 196 mowers
D. 31 304 mowers
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