Let
- Find the standard deviation of
. (1 mark)
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- Find
. (2 marks)
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Let
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a.
b.
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Mika is flipping a coin. The unbiased coin has a probability of
Let
Mika flips the coin five times.
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The height reached by each of Mika's coin flips is given by a continuous random variable,
where
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a. i.
a. iv
b. i.
b. ii.
b. iii.
c. i.
a.i
a.ii By CAS:
a.iii
By CAS:
a.iv
b.i
b.ii By CAS:
b.iii
c.i
The number of coin flips must be zero or a positive integer so
c.ii
c.iii To halve the width of the confidence interval, the standard deviation needs to be halved.
She would need to flip the coin 100 times
The Lorenz birdwing is the largest butterfly in Town A.
The probability density function that describes its life span,
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The wingspans of Lorenz birdwing butterflies in Town A are normally distributed with a mean of 14.1 cm and a standard deviation of 2.1 cm.
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Find the greatest possible wingspan, in centimetres, for a very small Lorenz birdwing butterfly in Town A, correct to one decimal place. (1 mark)
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Each year, a detailed study is conducted on a random sample of 36 Lorenz birdwing butterflies in Town A.
A Lorenz birdwing butterfly is considered to be very large if its wingspan is greater than 17.5 cm. The probability that the wingspan of any Lorenz birdwing butterfly in Town A is greater than 17.5 cm is 0.0527, correct to four decimal places.
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Find the smallest value of
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In a particular sample of Lorenz birdwing butterflies from Town B, an approximate 95% confidence interval for the proportion of butterflies that are very large was calculated to be (0.0234, 0.0866), correct to four decimal places.
Determine the sample size used in the calculation of this confidence interval. (2 marks)
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d.
e.
f.i.
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f.iv.
g.