Review
Review
A patient was given an injection of 500 mg of a medicine.
Every hour the amount of the medicine in the blood falls by 15%.
What is the decay factor?
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How many mg of the medicine will be in the blood after 4 hours? Round to a whole number.
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The doctor gives another injection when less than 200 mg is left in the blood.
After how many whole hours does the amount first fall below 200 mg? Try a few numbers of hours.
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A hospital received 80 mg of a radioactive substance for scans.
The substance’s half-life is 6 hours.
How many mg of the substance will be left after 24 hours?
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After how many hours will 2.5 mg be left?
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The graph: the number of insects in a colony, weeks from the start of the count.
Every week the number of insects is multiplied by the same number.
Write the formula of the graph.
Two towns have 20,000 residents each today.
In town A the number of residents grows by 1,000 every year.
In town B the number of residents grows by 4% every year.
How many residents will town A have in 10 years?
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How many residents will town B have in 10 years? Round to a whole number.
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Which town will have more residents in 30 years? Explain with a calculation.
Two machines fill 500-gram bags of rice.
Five bags from each machine were weighed, in grams:
| Bag 1 | Bag 2 | Bag 3 | Bag 4 | Bag 5 | |
|---|---|---|---|---|---|
| Machine A | 498 | 502 | 500 | 497 | 503 |
| Machine B | 490 | 510 | 500 | 495 | 505 |
Work out the mean of machine A’s bags. (Machine B’s mean is 500 grams.)
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Work out the standard deviation of machine A’s bags. Round to two decimal places.
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The standard deviation of machine B is about 7.07 grams.
Which machine is more precise? Explain.
20 pupils were asked how many brothers and sisters they have:
| Brothers and sisters | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Pupils | 4 | 10 | 4 | 2 |
Work out the mean.
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Work out the standard deviation. Round to two decimal places.
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A quiz has three true / false questions.
Dana did not study, and she guesses the answer to each question, with probability of a right answer.
Write the probabilities on the branches and the probability of each path.
What is the probability that Dana answers all three questions right?
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What is the probability that Dana answers at least one question right?
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200 patients took part in a trial of a new medicine.
Half of them were given the medicine, and half a placebo – a pill with no active substance.
| Improved | Did not improve | Total | |
|---|---|---|---|
| Given the medicine | 70 | 30 | 100 |
| Given a placebo | 40 | 60 | 100 |
| Total | 110 | 90 | 200 |
One participant is chosen at random.
What is the probability that the participant improved?
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The participant is known to have been given the medicine. What is the probability that they improved?
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The participant is known to have improved. What is the probability that they were given the medicine?
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Are the events “improved” and “given the medicine” dependent? Explain with your answers to parts a and b.
At the school fair you pay 10 ₪ and roll a die.
A 6 – you get 30 ₪.
A 5 – you get 15 ₪.
Any other number – you get nothing.
What is the expected value of the amount you get in one game?
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What is the expected value of a player’s gain in one game – the amount received minus 10 ₪?
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Is the game fair? How much should a 6 pay for the game to be fair?
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