1. Mathematical Treasure-hunt: Normal Distribution
Cut out each of the question slides and place them around the room.
Print out and distribute the answer sheet, one per pupil, or team, and set them off to find the answers.
The correct sequence is:
44, 2512,12.89, 400, 60.36, 2500, 178, , 30.7, 0.8, 2475, 1141

2. 35% of the components to last?
Mathematical Treasure-hunt: 44
Previous Answer ?
To the next clue
Mathematical Treasure-hunt:
2512
Previous Answer ?
To the next clue
The lifetime of an electrical component may be modelled by a Normal distribution with mean 2500 hours and variance 900 hour2. How long would you expect
35% of the components to last?
The length of a component may be modelled by a Normal distribution with standard deviation 3 cm. 15% of the components are longer than 16 cm. Calculate the mean length.

3. Mathematical Treasure-hunt:
12.89
Previous Answer ?
To the next clue
Mathematical Treasure-hunt:
400
Previous Answer ?
To the next clue
Assume that the lifetime of a certain type of light bulb may be modelled by a Normal distribution. It is found that 7% of the bulbs last for more than 1230 hours and 12% for less than 1070 hours. What is the standard deviation of the lifetime of these bulbs?
The weight of the contents of a jar may be modelled by a Normal distribution. 18% weigh more than 428g and 30% weigh more than 416g. Find the mean.

4. 50% of the components to last?
Mathematical Treasure-hunt: Sequences
60.36
Previous Answer ?
To the next clue
Mathematical Treasure-hunt: Sequences
2500
Previous Answer ?
To the next clue
The lifetime of an electrical component may be modelled by a Normal distribution with mean 2500 hours and variance 900 hour2. How long would you expect
50% of the components to last?
The quartiles of a Normal distribution are known to be 35 and 53. Find the variance of the distribution.

5. Mathematical Treasure-hunt: Sequences
178
Previous Answer ?
To the next clue
Mathematical Treasure-hunt: Sequences
0.0418
Previous Answer ?
To the next clue
Packets of currants are nominally 500g in weight. The actual weights may be modelled by a Normal distribution with mean 508.3g and standard deviation 4.8g. What is the probability that a packet is underweight?
The weight of the contents of a jar may be modelled by a Normal distribution. 18% weigh more than 428g and 30% weigh more than 416g. Find the standard deviation of the weight.

6. Mathematical Treasure-hunt: Sequences
30.7
Previous Answer ?
To the next clue
Mathematical Treasure-hunt: Sequences
0.8
Previous Answer ?
To the next clue
A factory produces a very large number of rods. The lengths of these rods may be modelled by a Normal distribution, with 30% of them measuring 30.6 cm or more and 15% of them measuring 29.2 cm or less.
Estimate the proportion of rods which measure 29.9 cm or more.
The lifetime of an electrical component may be modelled by a Normal distribution with mean 2500 hours and variance 900 hour2. How long would you expect
80% of the components to last?

7. Mathematical Treasure-hunt:
2475
Previous Answer ?
To the next clue
Mathematical Treasure-hunt:
1141
Previous Answer ?
To the next clue
Assume that the lifetime of a certain type of light bulb may be modelled by a Normal distribution. It is found that 7% of the bulbs last for more than 1230 hours and 12% for less than 1070 hours. What is the mean of the lifetime of these bulbs?
The quartiles of a Normal distribution are known to be 35 and 53. Find the mean of the distribution.

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