This discussion is now closed.

Check out other Related discussions

- Cie as level statistics question , please help
- Is this stats answer wrong?
- OCR S1 May 2006 Q7 - mean and standard deviation
- HELPPP A level maths linear interpolation
- Binomial distribution
- Integration by substitution (help)
- Relationships
- June 2018 Stats
- What would civilisation look like if the average IQ was 150?
- Maths paper 3 a level AQA
- Transforming normal distribution
- Probability distribution
- Central Limit Theorem: How do you calculate the test statistic?
- Hypothesis Testing
- GCSE
- Negative Binomial Question
- Hypothesis Testing
- Edexcel A Level Mathematics Paper 3 (9MA0 03) - 20th June 2024 [Exam Chat]
- Negative Binomial Question
- AQA A-level Mathematics Paper 3 (7357/3) - 20th June 2024 [Exam Chat]

i no this is probably simple, but i can't seem to b able to do this normal distribution question . . . .

The random variable X has a normal distribution with mean 16 and variance 0.64. Find x, such that P(X=x) = 0.025

can someone please help me

The random variable X has a normal distribution with mean 16 and variance 0.64. Find x, such that P(X=x) = 0.025

can someone please help me

Are you sure it says 'X=x' and not X<x or X>x, as far as I remember you couldnt get equalities using the normal distribution.

Statistical tables say that Phi(1.960) = 0.975. [Phi is the Greek letter $\Phi$.]

So there is probability 0.025 that a normal random variable is more than 1.960 standard deviations below its mean. [There is also probability 0.025 that a normal random variable is more than 1.960 standard deviations above its mean. But we don't need that for this question.]

So x = mean - 1.960*sd = 16 - 1.960*0.8 = 14.432.

So there is probability 0.025 that a normal random variable is more than 1.960 standard deviations below its mean. [There is also probability 0.025 that a normal random variable is more than 1.960 standard deviations above its mean. But we don't need that for this question.]

So x = mean - 1.960*sd = 16 - 1.960*0.8 = 14.432.

X~N (16 , 0.64)

P(X < x) = 0.025

An alternative to this is by looking at the percentage tables, it tells us that when p = 0.025, z = 1.9600. Since we are looking at the left of the normal distribution, the z value is negative (see attached image).

Therefore:

P(X < x)

= P(Z< x – 16 / √0.64 ) = -1.96

x – 16 = -1.96 * √0.64

x = -1.568 + 16

x = 14.432

P(X < x) = 0.025

An alternative to this is by looking at the percentage tables, it tells us that when p = 0.025, z = 1.9600. Since we are looking at the left of the normal distribution, the z value is negative (see attached image).

Therefore:

P(X < x)

= P(Z< x – 16 / √0.64 ) = -1.96

x – 16 = -1.96 * √0.64

x = -1.568 + 16

x = 14.432

- Cie as level statistics question , please help
- Is this stats answer wrong?
- OCR S1 May 2006 Q7 - mean and standard deviation
- HELPPP A level maths linear interpolation
- Binomial distribution
- Integration by substitution (help)
- Relationships
- June 2018 Stats
- What would civilisation look like if the average IQ was 150?
- Maths paper 3 a level AQA
- Transforming normal distribution
- Probability distribution
- Central Limit Theorem: How do you calculate the test statistic?
- Hypothesis Testing
- GCSE
- Negative Binomial Question
- Hypothesis Testing
- Edexcel A Level Mathematics Paper 3 (9MA0 03) - 20th June 2024 [Exam Chat]
- Negative Binomial Question
- AQA A-level Mathematics Paper 3 (7357/3) - 20th June 2024 [Exam Chat]

Latest

Trending

Last reply 3 weeks ago

How do l find the min & max radius of a circle on an argand diagramMaths

2

4