Answer all questions show your way clearly
1. (a) What proportion of a normal distribution is within one standard deviation of the
mean? (b) What proportion is more than 1.8 standard deviations from the mean? (c) What
proportion is between 1 and 1.5 standard deviations above the mean?
2. A test is normally distributed with a mean of 40 and a standard deviation of 7. (a) What
score would be needed to be in the 85th percentile? (b) What score would be needed to be
in the 22nd percentile?
3. Assume a normal distribution with a mean of90 and a standard deviation of7. What
limits would include the middle 65% of the cases.
4.Suppose that a local study finds that 90% of people aged over 60 years in
Windhoek city suffer from at least one common cold during a one-year period,
and 20% suffer from heartburn at least once.
(a)What is the probability that any person over 60 years of age will suffer from either common
cold or heartburn? We shall assume that common cold and heartburn occur independently of
each other. 10 marks
5.The probability of three teams A,B, and C winning a football competition are 1/3,1I5,and 1/9
respectively. Calculate the possibility that;
(a) Either A or B will win - 4 marks
(b) Either A or B or C will win- 4 marks
(c) None of these three teams will win- 6 marks
(d) Neither A nor B will win- 6 marks
6. Suppose we want to estimate the average weight of an adult male in Namibia. We draw a
random sample of 1,000 men from a population of 1,000,000 men and weigh them. We find that
the average man in our sample weighs 180 pounds, and the standard deviation of the sample is
30 pounds. What is the 95% confidence interval.
(a) 180 ± 1.86
(b) 180 ± 3.0
(c) 180 ± 5.88
(d) 180±30
(e) None of the above 7