IB Mathematics Analysis and Approaches Topic SL 4.9—normal Distribution and Calculations Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 4.9—normal Distribution and Calculations Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 4.9—normal Distribution and Calculations with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 4.9—normal Distribution and Calculations and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 2

A clinic measures the systolic blood pressure of all visiting patients. The blood pressure $P$ , in mmHg, of patients is normally distributed with a mean of $122$ mmHg and a standard deviation of $9$ mmHg. A patient is classified as having elevated blood pressure if $P > 130$ mmHg.

A patient is selected at random.

Find the probability that this patient has elevated blood pressure.

[3]

Given that the patient has elevated blood pressure, find the probability that their blood pressure is greater than $140$ mmHg.

[3]

Two patients are selected at random. Find the probability that they both have elevated blood pressure.

[3]

Three hundred patients are selected at random.

Find the probability that at least $50$ of these $300$ patients have elevated blood pressure.

[4]

Three hundred patients are selected at random.

Find the expected number of patients with elevated blood pressure among these $300$ patients.

[2]

Question 2

HLPaper 2

The weights $W$ , in grams, of apples from a farm are normally distributed with mean $185$ g and standard deviation $22$ g.

Find the probability that a randomly selected apple weighs between $170$ g and $200$ g.

[2]

Find the value of $w$ such that $5%$ of apples weigh more than $w$ g.

[3]

Find the probability that a randomly chosen apple is small.

[4]

Find the probability that a randomly chosen apple is large.

[4]

Find the probability that a randomly chosen apple is medium.

[4]

Four apples are randomly selected, independently. Find the probability that exactly two are small and exactly two are medium.

[4]

A random sample of $400$ apples is selected. Find the expected number of large apples in the sample.

[2]

A randomly selected apple is found to be heavier than the mean. Find the probability that this apple is large.

[3]

Find the smallest sample size $n$ such that the probability of obtaining at least one large apple in the sample exceeds $0.99$ .

[2]

Question 3

SLPaper 2

A bakery produces loaves of bread. The weights $X$ , in grams, of loaves can be modelled by a normal distribution where $X \sim N (μ, σ^{2})$ . A loaf is classified as substandard if it weighs less than $480$ grams.

Given that $μ = 510$ and $σ = 12$ , find the probability that a randomly selected loaf is substandard.

[2]

The bakery decides that the probability that a loaf is substandard should be $0.0008$ . To do this $μ$ is increased and $σ$ is kept unchanged.

Calculate the new value of $μ$ , rounding your answer to the nearest gram.

[3]

The bakery is happy with the decision that the probability that a loaf is substandard should be $0.0008$ , but is unhappy with the way in which this was achieved. The machines are now adjusted to reduce $σ$ and return $μ$ back to $510$ grams.

Calculate the new value of $σ$ , rounding your answer to the nearest gram.

[3]

Question 4

SLPaper 2

The lengths of fish caught in a lake are normally distributed with a mean of 45 cm and a standard deviation of 6 cm. A fish is considered large if its length exceeds 50 cm.

Calculate the probability that a randomly caught fish is large.

[2]

A fish is selected at random from those that are large. Find the probability that its length is more than 55 cm.

[4]

Estimate the interquartile range of the fish lengths.

[3]

Question 5

SLPaper 2

Let $X$ and $Y$ be normally distributed with $X \sim N (80, σ^{2})$ and $Y \sim N (56, σ^{2})$ , where the values are measured in kilograms.

Find $k$ such that $P (Y > k) = P (X < k)$ .

[2]

Given that $P (X > 76) = 0.7881$ , find $P (60 < Y < 65)$ .

[5]

IB Mathematics Analysis and Approaches SL 4.9—normal Distribution and Calculations Questionbank

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IB Mathematics Analysis and Approaches SL 4.9—normal Distribution and Calculations Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 4.9—normal Distribution and Calculations Questionbank

Unlock all 13 questions with a free account