VCE Maths Methods resources!

BLOG HAS BEEN MOVED!

flusher317 — Tue, 23 Sep 2008 16:48:22 +0000

Sorry guys

this blog has been moved to…

mathsmethods.blogspot.com

Tell all your methods friends about it so that they can kick some ass too in methods!

regards

David

Probability (Normal) Tough Question 5

flusher317 — Sun, 21 Sep 2008 02:08:17 +0000

In a given manufacturing process, components are rejected if they have a particular
dimension greater than 60.4 mm or less than 59.7 mm. It is found that 3% are rejected as
being too large and 5% are rejected for being too small. Assume that the dimension is
normally distributed.

a. Find the mean and standard deviation of the distribution of the dimension, correct to
one decimal place.

b. Use the result of a to find the percentage of rejects if the limits for acceptance are
changed to 60.3 mm and 59.6 mm.

Probability (Normal) Standard Question 3

flusher317 — Sun, 21 Sep 2008 02:05:56 +0000

The hardness of a metal may be determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose that the hardness of a particular alloy is normally distributed with mean 70 and standard deviation 3.

a. If a specimen is acceptable only if its hardness is between 65 and 75, what is the
probability that a randomly chosen specimen has an acceptable hardness?

b. If the acceptable range of hardness was (70 − c, 70 + c), for what value of c would 95%
of all specimens have acceptable hardness?

c. If the acceptable range is the same as in a, and the hardness of each of 10 randomly
selected specimens is independently determined, what is the expected number of
acceptable specimens among the 10?

d. What is the probability that at most eight out of 10 independently selected specimens
have a hardness less than 73.84?

e. The profit on an acceptable specimen is $20.00, while unacceptable specimens result in
a loss of $5.00. If P dollars is the profit on a randomly selected specimen, find the mean
and variance of P.

Probability (Normal) Tough Question 4

flusher317 — Sun, 21 Sep 2008 02:00:52 +0000

Suppose that L, the useful life (in hours) of a fluorescent tube used for indoor gardening, is normally distributed with a mean of 600 and a standard deviation of 4. The fluorescent tubes are sold in boxes of 10. Find the probability that at least three of the tubes in a randomly selected box last longer than 605 hours.

Probability (Normal) Standard Question 2

flusher317 — Sun, 21 Sep 2008 01:45:52 +0000

The owner of a new van complained to the dealer that he was using, on average, 18 litres petrol to drive 100 km. The dealer pointed out that the 15 litres/100 km referred to in an advertisement was ‘just a guide and that actual consumption will vary’. Suppose that the distribution of fuel consumption for this make of van is normal with a mean of 15 litres/100 km and standard deviation 0.75 litres/100 km.

a. How probable is a van that uses at least 18 litres/100 km?

b What does your answer to a suggest about the manufacturer’s claim?

c Find c1 and c2 such that the van’s fuel consumption is more than c1 but less than c2 a probability of 0.95.

Probability (Normal) Standard Question 1

flusher317 — Sun, 21 Sep 2008 01:38:17 +0000

Potatoes are delivered to a chip factory in semitrailer loads. A sample of 1 kg of the potatoes is chosen from each load and tested for starch content. From past experience it is known that the starch content is normally distributed with a standard deviation 2.1.

If the starch content is greater than 22.0 the potatoes cannot be used for chips, so the semitrailer load is rejected. What is the probability that a load with mean starch content of 18.0 will be rejected?

Probability (Normal) Tough Question 3

flusher317 — Sat, 20 Sep 2008 16:41:39 +0000

The strength of a certain fibre (fibre A) is normally distributed with mean of 45 and standard deviation of 6. The strength of another fibre (fibre B) is also normally distributed with mean of 53 and standard deviation of 5. Now to determine whether a piece of fibre is either A or B, the strength of it is tested. If the strength is lower than a specific value “m”, than it is an A fibre. All other cases would then be type B. For a piece of fibre to be misclassified, it must be in the wrong classification.

The question is, find the value of “m” for which the two probabilities of misclassification are equal!

Probability (Normal) Tough Question 2

flusher317 — Mon, 15 Sep 2008 03:32:55 +0000

The volume of Cola in a particular 350ml can is normally distributed. If there is more than a 5% chance of a can of Cola having less than 347ml, then a fine will be issued. The standard deviation for the amount of Cola in these cans is 2.3ml. The question is, what should the minimum target filling volume (Mean) be, provided that we don’t want any fines to be issued?

Probability (Normal) Tough question 1

flusher317 — Mon, 15 Sep 2008 03:29:40 +0000

The weight of all pugs is normally distributed. 13% of all pugs are under the weight of 7.46Kg, and 17% of all pugs are above the weight of 10.34Kg.

Find the mean, and standard deviation.

How does Maths Methods Scale?

flusher317 — Mon, 15 Sep 2008 03:05:05 +0000

Raw Score	Scaled Score
	Further Maths	Maths Methods	Maths Methods (CAS)	Specialist Maths
30	28	37	37	40
35	33	41	42	45
40	38	45	46	49
45	44	48	48	52
50	50	50	50	55

These figures are only approximates, averaged out from the past 5 years!