• Syllabus

4.1

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Sub sections and their related questions

The normal distribution.

• SPM.2.sl.TZ0.3a: Sketch a diagram of the distribution of the weight of Brahma chicken eggs. On your diagram, show...
• SPM.2.sl.TZ0.3d: The probability that a Brahma chicken produces a large size egg is \(0.121\). Frank’s Brahma...
• SPM.2.sl.TZ0.3e: The selling price, in US dollars (USD), of each size is shown in the table below.The probability...
• 14M.2.sl.TZ1.5a: Draw a diagram that shows this information.
• 14N.1.sl.TZ0.12a: Calculate the probability that the temperature on a randomly chosen day in January is less than...
• 14N.1.sl.TZ0.12b: Calculate the expected number of days in January that the temperature will be more than 39°C.
• 14N.1.sl.TZ0.12c: On a randomly chosen day in January, the probability that the temperature is above \(T\) °C is...
• 15M.1.sl.TZ1.13a: Find the probability that a bag of rice chosen at random weighs between 990 g and 1004 g.
• 15M.1.sl.TZ1.13b: 95% of the bags of rice weigh less than \(k\) grams. Find the value of \(k\).
• 15M.1.sl.TZ1.13c: For a bag of rice chosen at random, \({\text{P}}(1000 - a < W < 1000 + a) = 0.9\). Find...
• 15M.1.sl.TZ2.13a: On the following diagram, shade the region representing the probability that a metal bar, chosen...
• 15M.1.sl.TZ2.13b: A metal bar is chosen at random. (i)     The probability that the length of the metal bar is...
• 15M.2.sl.TZ2.4b: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 15M.2.sl.TZ2.4c: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 15M.2.sl.TZ2.4d: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 15M.2.sl.TZ2.4e: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 16M.1.sl.TZ1.8a: The lifetime, \(L\) , of light bulbs made by a company follows a normal distribution.\(L\) is...
• 16M.1.sl.TZ1.8b: The standard deviation of the lifetime of the light bulbs is \(850\) hours. Find the probability...
• 16M.1.sl.TZ1.8c: The company states that \(90\% \) of the light bulbs have a lifetime of at least...
• 16N.2.sl.TZ0.4a: Draw a diagram that shows this information.
• 16N.2.sl.TZ0.4b: (i)     Find the probability that a box of cereal, chosen at random, is sold. (ii)     Calculate...
• 16N.2.sl.TZ0.4c: Calculate the manufacturer’s expected daily recycling cost.
• 16N.2.sl.TZ0.4d: Calculate the value of \(w\).
• 16M.2.sl.TZ2.3a: A speed camera on Peterson Road records the speed of each passing vehicle. The speeds are found...
• 16M.2.sl.TZ2.3b: A vehicle on Peterson Road is chosen at random. Find the probability that the speed of this...
• 16M.2.sl.TZ2.3c: It is found that \(19\,\% \) of the vehicles are exceeding the speed limit of...
• 16M.2.sl.TZ2.3d: There is a fine of \({\text{US}}\$ 65\) for exceeding the speed limit on Peterson Road. On a...
• 17N.1.sl.TZ0.13a: Find the probability that this applicant took at least 40 minutes to complete the test.
• 17N.1.sl.TZ0.13b: Find the value of \(k\).
• 17N.1.sl.TZ0.13c: Estimate the number of applicants who completed the test in less than 25 minutes.
• 18M.2.sl.TZ2.3a.i: Find the probability that a basketball player has a weight that is less than 61 kg.
• 18M.2.sl.TZ2.3a.ii: In a training session there are 40 basketball players. Find the expected number of players with...
• 18M.2.sl.TZ2.3b.i: Sketch a normal curve to represent this probability.
• 18M.2.sl.TZ2.3b.ii: Find the value of q.
• 18M.2.sl.TZ2.3c: Given that P(W > k) = 0.225 , find the value of k.
• 18M.2.sl.TZ2.3d.i: For this test state the null hypothesis.
• 18M.2.sl.TZ2.3d.ii: For this test find the p-value.
• 18M.2.sl.TZ2.3e: State a conclusion for this test. Justify your answer.

The concept of a random variable; of the parameters \(\mu \) and \(\sigma \) ; of the bell shape; the symmetry about \(x = \mu \) .

• SPM.2.sl.TZ0.3a: Sketch a diagram of the distribution of the weight of Brahma chicken eggs. On your diagram, show...
• 14M.2.sl.TZ1.5a: Draw a diagram that shows this information.
• 14N.1.sl.TZ0.12a: Calculate the probability that the temperature on a randomly chosen day in January is less than...
• 15M.1.sl.TZ1.13a: Find the probability that a bag of rice chosen at random weighs between 990 g and 1004 g.
• 15M.1.sl.TZ1.13c: For a bag of rice chosen at random, \({\text{P}}(1000 - a < W < 1000 + a) = 0.9\). Find...
• 15M.1.sl.TZ2.13a: On the following diagram, shade the region representing the probability that a metal bar, chosen...
• 18M.2.sl.TZ2.3a.i: Find the probability that a basketball player has a weight that is less than 61 kg.
• 18M.2.sl.TZ2.3a.ii: In a training session there are 40 basketball players. Find the expected number of players with...
• 18M.2.sl.TZ2.3b.i: Sketch a normal curve to represent this probability.
• 18M.2.sl.TZ2.3b.ii: Find the value of q.
• 18M.2.sl.TZ2.3c: Given that P(W > k) = 0.225 , find the value of k.
• 18M.2.sl.TZ2.3d.i: For this test state the null hypothesis.
• 18M.2.sl.TZ2.3d.ii: For this test find the p-value.
• 18M.2.sl.TZ2.3e: State a conclusion for this test. Justify your answer.

Diagrammatic representation.

• SPM.2.sl.TZ0.3a: Sketch a diagram of the distribution of the weight of Brahma chicken eggs. On your diagram, show...
• 14M.2.sl.TZ1.5a: Draw a diagram that shows this information.
• 15M.1.sl.TZ1.13b: 95% of the bags of rice weigh less than \(k\) grams. Find the value of \(k\).
• 15M.1.sl.TZ1.13c: For a bag of rice chosen at random, \({\text{P}}(1000 - a < W < 1000 + a) = 0.9\). Find...
• 15M.1.sl.TZ2.13a: On the following diagram, shade the region representing the probability that a metal bar, chosen...
• 15M.2.sl.TZ2.4b: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 15M.2.sl.TZ2.4c: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 18M.2.sl.TZ2.3a.i: Find the probability that a basketball player has a weight that is less than 61 kg.
• 18M.2.sl.TZ2.3a.ii: In a training session there are 40 basketball players. Find the expected number of players with...
• 18M.2.sl.TZ2.3b.i: Sketch a normal curve to represent this probability.
• 18M.2.sl.TZ2.3b.ii: Find the value of q.
• 18M.2.sl.TZ2.3c: Given that P(W > k) = 0.225 , find the value of k.
• 18M.2.sl.TZ2.3d.i: For this test state the null hypothesis.
• 18M.2.sl.TZ2.3d.ii: For this test find the p-value.
• 18M.2.sl.TZ2.3e: State a conclusion for this test. Justify your answer.

Normal probability calculations.

• SPM.2.sl.TZ0.3b: An egg is chosen at random. Find the probability that the egg is(i)     medium;(ii)    extra large.
• 14M.1.sl.TZ2.14a: Write down the probability that a randomly chosen tree has a height greater...
• 14M.1.sl.TZ2.14b: Write down the probability that a randomly chosen tree will be within 2 standard deviations of...
• 14M.1.sl.TZ2.14c: Use your graphic display calculator to calculate the probability that a randomly chosen tree will...
• 14M.2.sl.TZ1.5b: Write down the probability that a randomly chosen candidate who sat the Chemistry examination...
• 14M.2.sl.TZ1.5c: Hee Jin scored 80 marks in the Chemistry examination. Find the probability that a randomly...
• 14M.2.sl.TZ1.5d: The candidates’ marks in the Physics examination are normally distributed with a mean of \(63\)...
• 14M.2.sl.TZ1.5e: The candidates’ marks in the Physics examination are normally distributed with a mean of \(63\)...
• 14N.1.sl.TZ0.12a: Calculate the probability that the temperature on a randomly chosen day in January is less than...
• 15M.1.sl.TZ1.13a: Find the probability that a bag of rice chosen at random weighs between 990 g and 1004 g.
• 15M.1.sl.TZ2.13b: A metal bar is chosen at random. (i)     The probability that the length of the metal bar is...
• 15M.2.sl.TZ2.4b: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 15M.2.sl.TZ2.4d: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 18M.2.sl.TZ2.3a.i: Find the probability that a basketball player has a weight that is less than 61 kg.
• 18M.2.sl.TZ2.3a.ii: In a training session there are 40 basketball players. Find the expected number of players with...
• 18M.2.sl.TZ2.3b.i: Sketch a normal curve to represent this probability.
• 18M.2.sl.TZ2.3b.ii: Find the value of q.
• 18M.2.sl.TZ2.3c: Given that P(W > k) = 0.225 , find the value of k.
• 18M.2.sl.TZ2.3d.i: For this test state the null hypothesis.
• 18M.2.sl.TZ2.3d.ii: For this test find the p-value.
• 18M.2.sl.TZ2.3e: State a conclusion for this test. Justify your answer.

Expected value.

• SPM.2.sl.TZ0.3d: The probability that a Brahma chicken produces a large size egg is \(0.121\). Frank’s Brahma...
• SPM.2.sl.TZ0.3e: The selling price, in US dollars (USD), of each size is shown in the table below.The probability...
• 14N.1.sl.TZ0.12b: Calculate the expected number of days in January that the temperature will be more than 39°C.
• 15M.2.sl.TZ2.4e: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 18M.2.sl.TZ2.3a.i: Find the probability that a basketball player has a weight that is less than 61 kg.
• 18M.2.sl.TZ2.3a.ii: In a training session there are 40 basketball players. Find the expected number of players with...
• 18M.2.sl.TZ2.3b.i: Sketch a normal curve to represent this probability.
• 18M.2.sl.TZ2.3b.ii: Find the value of q.
• 18M.2.sl.TZ2.3c: Given that P(W > k) = 0.225 , find the value of k.
• 18M.2.sl.TZ2.3d.i: For this test state the null hypothesis.
• 18M.2.sl.TZ2.3d.ii: For this test find the p-value.
• 18M.2.sl.TZ2.3e: State a conclusion for this test. Justify your answer.

Inverse normal calculations.

• SPM.2.sl.TZ0.3c: There is a probability of \(0.3\) that a randomly chosen egg weighs more than \(w\) grams. Find...
• 14M.1.sl.TZ2.14d: The probability that a particular tree is less than \(x\) metres high is \(0.65\). Find the value...
• 14M.2.sl.TZ1.5f: To obtain a “grade A” a candidate must be in the top \(10\% \) of the candidates who sat the...
• 14N.1.sl.TZ0.12c: On a randomly chosen day in January, the probability that the temperature is above \(T\) °C is...
• 15M.1.sl.TZ1.13b: 95% of the bags of rice weigh less than \(k\) grams. Find the value of \(k\).
• 15M.1.sl.TZ1.13c: For a bag of rice chosen at random, \({\text{P}}(1000 - a < W < 1000 + a) = 0.9\). Find...
• 15M.1.sl.TZ2.13b: A metal bar is chosen at random. (i)     The probability that the length of the metal bar is...
• 15M.2.sl.TZ2.4c: Daniel assumes that the diameters of all of the apples from his harvest are normally distributed...
• 18M.2.sl.TZ2.3a.i: Find the probability that a basketball player has a weight that is less than 61 kg.
• 18M.2.sl.TZ2.3a.ii: In a training session there are 40 basketball players. Find the expected number of players with...
• 18M.2.sl.TZ2.3b.i: Sketch a normal curve to represent this probability.
• 18M.2.sl.TZ2.3b.ii: Find the value of q.
• 18M.2.sl.TZ2.3c: Given that P(W > k) = 0.225 , find the value of k.
• 18M.2.sl.TZ2.3d.i: For this test state the null hypothesis.
• 18M.2.sl.TZ2.3d.ii: For this test find the p-value.
• 18M.2.sl.TZ2.3e: State a conclusion for this test. Justify your answer.