Test 2a Math 1P98 Nov 18 2005 5:15 to 6:15
Name
........................................
Student Number
.......................
BOX Number
.........
You may bring one sheet of coloured paper handwritten with no xerox, or printing of any
kind.
Calculators must have no more than two lines of display.
Answers must have at
least 3 sig dig, however numbers taken from Minitab output should keep all their digits.
Good Luck
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[12]
1a.
The length of ladybugs forms a
normal distribution. How many ladybugs would
have to
observe to be 98% sure of being within 0.1 mm of their mean length?
A
sample of 32 ladybugs gave a mean length of 5.6 mm with standard deviation 0.3 mm.
b.
The fully grown ladybug of the type
Harmonia axyridis
that tries to come indoors in
winter has a maximum of 10 spots on each wing. To investigate the proportion of these
ladybugs that have the full number of spots and to be within 5% of the true proportion
with 90% confidence, how many ladybugs would have to be studied?
c.
For a given location it is found that 40% of these ladybugs survive the winter by
finding a sheltered place. If 80 hibernate in a garage, to calculate the probability that
less than 20 survive, using the normal approximation to the binomial, the z score is:
, where a =
........
b =
........
and c =
........
( give numeric answers)
d.
The population mean is 5.6 mm and the standard deviation is 0.3 mm. In order to
find the probability that the mean length of 10 of these ladybugs was greater than 6
mm, we calculate the z score as :
where a =
........
b =
........
and c =
........
( give numeric answers)

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