STAT170 Workshop Notes prepared by Nan Carter for Numeracy ...

CHECKS: Q1: a) 0.9104 b) 0.1525 c) 0.0401 Q2: a) 1.16
b) 0.3770 c) 0.3770 Q3: 7.05 and 2.05 Q4: a) 2.08 b) 120
c) 0.3372 d) 0.0188 Q5: 29 ; 27 Q6: a) 0.0764 b) 0.2389
c) 0.6847 d) 0.77 Q7: a) 0.1587 b) 1.88
ALL the questions on this page need to be interpreted as finding z-values, y-values or
probabilities (i.e. area under the standard normal curve). The calculations that you
need have already been done above; BUT, not all the above answers are needed, AND
the order of the questions has been scrambled.
1. The height of adult women in Australia is approx normally distributed with mean
μ=160cm, and standard deviation σ=7cm.
a) What is the probability that a single randomly selected woman has height
between 150cm and 165cm?
b) What is the probability that a randomly selected woman has a height less than
or equal to your own height? (eg my height is 158cm).
c) What is the greatest height exceeded by 22% of the population of adult women?
2. The useful life of a certain brand of batteries is normally distributed with a mean of
150 hours and a standard deviation of 24 hours. If a battery is selected at random,
find the probability that its useful life is:
a) less than 100 hours
b) more than 120 hours
c) between 160 and 200 hours.
3. The weights of bags of fertiliser are normally distributed with mean 210 kg and
standard deviation of 2.3 kg. For a consignment of 150 bags, what is the expected
number of bags that will weigh less than 208 kg? How many of the bags weighing
less that 208 kg would be expected to weigh more than 205 kg?
4. A soft drink machine discharges on average 250ml per cup, with a standard
deviation of 14 ml. The ml of fill is approximately normally distributed.
e) What is the probability of overfilling a 264 ml cup?
f) How large a cup is required so that the probability that the cup will overflow is
only 3%?
5. The average life of an electric sandwich maker is 5 years with a standard deviation
of one year. If the manufacturer replaces free any appliance that fails while under
guarantee, how long a guarantee should be offered if the profit depends on no more
than 2% being replaced? (Assume lifetimes are normally distributed.)
CHECKS: Q1. a) 0.6847 b) for my height of 158cm: 0.3859 c) 165.4
Q2. a) 0.0188 b) 0.8944 c) 0.3184
Q3. 29 ; 27 Q4. a) 0.1587 b) 276 Q5. 7 years
4
Nan Carter: workshop notes prepared for Numeracy Centre Macquarie University.