DP Mathematics HL Questionbank

• Syllabus

5.7

Sub sections and their related questions

Normal distribution.

• 12M.2.hl.TZ1.12c: It is found that 20 % of skiers having accidents are at least 25 years of age and 40 % are under...
• 12M.2.hl.TZ2.10a: The weights of the apples are normally distributed with a mean of 200 grams and a standard...
• 12M.2.hl.TZ2.10b: The weights of the pears are normally distributed with a mean of ∝ grams and a standard deviation...
• 12M.2.hl.TZ2.10c: The weights of the plums are normally distributed with a mean of 80 grams and a standard...
• 12N.2.hl.TZ0.11d: The ages of the visitors to the museum can be modelled by a normal distribution with mean...
• 12N.2.hl.TZ0.11e: The ages of the visitors to the museum can be modelled by a normal distribution with mean...
• 08M.2.hl.TZ1.4: A company produces computer microchips, which have a life expectancy that follows a normal...
• 08M.2.hl.TZ2.11a: The distance travelled by students to attend Gauss College is modelled by a normal distribution...
• 08M.2.hl.TZ2.11b: At Euler College, the distance travelled by students to attend their school is modelled by a...
• 08N.2.hl.TZ0.11Part A: (a)     A box of biscuits is considered to be underweight if it weighs less than 228 grams. It is...
• 11M.2.hl.TZ2.6a: Determine the probability that a fish which is caught weighs less than 1.4 kg.
• 11M.3sp.hl.TZ0.1a: Find the probability that a randomly chosen orange weighs more than 200 grams.
• SPNone.2.hl.TZ0.12a: Given that 70 % of the birds weigh more than 2.1 kg and 25 % of the birds weigh more than 2.5 kg,...
• 13M.2.hl.TZ1.3a: Find the probability she is late next Monday.
• 10M.2.hl.TZ1.8: In a factory producing glasses, the weights of glasses are known to have a mean of 160 grams. It...
• 10M.2.hl.TZ2.3: After being sprayed with a weedkiller, the survival time of weeds in a field is normally...
• 10N.2.hl.TZ0.3: The weight loss, in kilograms, of people using the slimming regime SLIM3M for a period of three...
• 13M.2.hl.TZ2.3a: Calculate the range of lifespans of Manx cats whose lifespans are within one standard deviation...
• 13M.2.hl.TZ2.3b: Estimate the number of Manx cats in a population of 10 000 that will have a lifespan of less than...
• 11N.2.hl.TZ0.11a: In the past year, 80 % of Jan’s throws have been longer than x metres. Find x correct to two...
• 11N.2.hl.TZ0.11b: In the past year, 80 % of Sia’s throws have been longer than 56.52 metres. If the mean distance...
• 11N.2.hl.TZ0.11c: This year, Sia’s throws have a mean of 59.50 metres and a standard deviation of 3.00 metres. The...
• 11N.3sp.hl.TZ0.1a: Find the probability that a randomly chosen Supermug tea bag contains more than 3.9 g of tea.
• 11N.3sp.hl.TZ0.1b: Find the probability that, of two randomly chosen Megamug tea bags, one contains more than 5.4 g...
• 11M.2.hl.TZ1.12a: Find the mean and standard deviation of \(X\).
• 11M.2.hl.TZ1.12b: The school has 1200 students and classes start at 09:00. Estimate the number of students who will...
• 11M.2.hl.TZ1.12c: Maelis had not arrived by 08:30. Find the probability that she arrived late.
• 09N.2.hl.TZ0.6: (a)     Tim says he will leave if he is not seated at a table within \(25\) minutes of arriving...
• 09M.2.hl.TZ1.1: Bob measured the heights of 63 students. After analysis, he conjectured that the height, \(H\) ,...
• 09M.2.hl.TZ2.11: (a)     Show that the probability that a randomly selected bottle filled by Machine A contains...
• 14M.2.hl.TZ1.2: A student sits a national test and is told that the marks follow a normal distribution with mean...
• 14M.2.hl.TZ2.2: The weights, in kg, of one-year-old bear cubs are modelled by a normal distribution with mean...
• 13N.2.hl.TZ0.4: The duration of direct flights from London to Singapore in a particular year followed a normal...
• 14N.2.hl.TZ0.2a: Find the value of \(x\).
• 14N.2.hl.TZ0.2b: In a field experiment, a research team studies a large sample of these birds. The wingspans of...
• 15M.2.hl.TZ1.2a: Find the probability that a runner finishes the race in under three hours.
• 15M.2.hl.TZ1.2b: The fastest \(90\% \) of the finishers receive a certificate. Find the time, below which a...
• 15M.2.hl.TZ2.10a: Farmer Suzie grows turnips and the weights of her turnips are normally distributed with a mean of...
• 15M.3sp.hl.TZ0.1a: A large can is selected at random. Find the probability that the can contains at least \(4995\)...
• 15N.2.hl.TZ0.11a: (i)     Determine two simultaneous linear equations satisfied by \(\mu \) and \(\sigma \). (ii)...
• 15N.2.hl.TZ0.11b: Find the probability that an office worker weighs more than \(100\) kg.
• 16M.2.hl.TZ1.6: The heights of students in a single year group in a large school can be modelled by a normal...
• 16M.2.hl.TZ2.2a: Find \({\text{P}}(0 \leqslant X \leqslant 2)\).
• 16M.2.hl.TZ2.2b: Find \({\text{P}}(\left| X \right| > 1)\).
• 16M.2.hl.TZ2.2c: If \({\text{P}}(X > c) = 0.44\), find the value of \(c\).
• 16N.2.hl.TZ0.8a: Find \(\mu \) and \(\sigma \).
• 16N.2.hl.TZ0.8b: Find \({\text{P}}\left( {\left| {X - \mu } \right| < 1.2\sigma } \right)\).
• 17N.2.hl.TZ0.4: It is given that one in five cups of coffee contain more than 120 mg of caffeine.It is also known...
• 18M.2.hl.TZ1.4a: Find the probability that a wolf selected at random is at least 5 years old.
• 18M.2.hl.TZ1.4b: Eight wolves are independently selected at random and their ages recorded. Find the probability...
• 18M.2.hl.TZ2.3a: Sketch the probability density function for X, and shade the region representing P(μ − 2σ < X...
• 18M.2.hl.TZ2.3b: Find the value of P(μ − 2σ < X < μ + σ).
• 18M.2.hl.TZ2.3c: Find the value of k for which P(μ − kσ < X < μ + kσ) = 0.5.

Properties of the normal distribution.

• 12M.2.hl.TZ2.10a: The weights of the apples are normally distributed with a mean of 200 grams and a standard...
• 12M.2.hl.TZ2.10b: The weights of the pears are normally distributed with a mean of ∝ grams and a standard deviation...
• 12M.2.hl.TZ2.10c: The weights of the plums are normally distributed with a mean of 80 grams and a standard...
• 11M.2.hl.TZ2.6a: Determine the probability that a fish which is caught weighs less than 1.4 kg.
• 15N.2.hl.TZ0.11a: (i)     Determine two simultaneous linear equations satisfied by \(\mu \) and \(\sigma \). (ii)...

Standardization of normal variables.

• 12M.2.hl.TZ2.10a: The weights of the apples are normally distributed with a mean of 200 grams and a standard...
• 12M.2.hl.TZ2.10b: The weights of the pears are normally distributed with a mean of ∝ grams and a standard deviation...
• 12M.2.hl.TZ2.10c: The weights of the plums are normally distributed with a mean of 80 grams and a standard...
• 11M.2.hl.TZ2.6a: Determine the probability that a fish which is caught weighs less than 1.4 kg.
• 15M.2.hl.TZ2.10b: Farmer Ray also grows turnips and the weights of his turnips are normally distributed with a mean...
• 15N.2.hl.TZ0.11a: (i)     Determine two simultaneous linear equations satisfied by \(\mu \) and \(\sigma \). (ii)...