anaindiemood
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If a group of children have a mean score of 108 and the variance is 169. What range would you expect 95% of the children to score within?
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Theloniouss
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Do you know what variance is? Is there any more context for this question?
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anaindiemood
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(Original post by Theloniouss)
Do you know what variance is? Is there any more context for this question?
Literally no more context that’s the whole question!
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arwaisfailing
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do you know what sort of distribution this is?
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anaindiemood
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(Original post by arwaisfailing)
do you know what sort of distribution this is?
Under a normal distribution
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arwaisfailing
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okay great, so do you know where to use this info in ur graphical calculator?
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anaindiemood
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(Original post by arwaisfailing)
okay great, so do you know where to use this info in ur graphical calculator?
Unfortunately not😬
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old_engineer
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(Original post by anaindiemood)
If a group of children have a mean score of 108 and the variance is 169. What range would you expect 95% of the children to score within?
To answer this question you probably have to assume that students' scores are normally distributed. You also have to guess whether the 95% of students means that 95% of students will score <= a particular score, or >= a particular score, or whether the 95% is supposed to be symmetrically arranged either side of the mean. I think the last of those options is most likely, in which case, the 5% of students not included in the central 95% will be divided equally between lower and upper tails of 2.5% each. What you then need to know is that, for a normal distribution, an upper tail of 2.5% starts 1.96 standard deviations above the mean, with similar reasoning for the lower tail. You will find these and similar % figures in a table of percentage points for the normal distribution, contained in textbooks and A level formula. booklets.
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arwaisfailing
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(Original post by anaindiemood)
Unfortunately not😬
okay so using a graphical calculator, go into the STATS section
then click F5 for DIST (distribution)
then click F1 for NORM (normal distribution)
then for this question, you need Ncd (normal cumulative distribution)

for all of this, if you have or don’t have any values in the table that shows, it makes no difference (so ignore & just follow what i’ve said above)

is this making sense? i want to help you guide urself to the answer rather than giving it to u straight so it’s helps a bit more, sorry if anything sounds patronising!!
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arwaisfailing
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really sorry, i didn’t read the question properly, pls click InvN, NOT Ncd
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anaindiemood
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(Original post by arwaisfailing)
okay so using a graphical calculator, go into the STATS section
then click F5 for DIST (distribution)
then click F1 for NORM (normal distribution)
then for this question, you need Ncd (normal cumulative distribution)

for all of this, if you have or don’t have any values in the table that shows, it makes no difference (so ignore & just follow what i’ve said above)

is this making sense? i want to help you guide urself to the answer rather than giving it to u straight so it’s helps a bit more, sorry if anything sounds patronising!!
Not at all! I appreciate your help so much! However my calculator isn’t like that. When I go onto the distribution setting it comes up with a list of normal PD, normal CD, inverse normal, binomial PD etc...
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arwaisfailing
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that’s okay, InvN just means inverse normal so just use that one
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arwaisfailing
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try plugging in ur values into that inverse normal section and tell me what u do, and i’ll lyk if your answer matches mine
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arwaisfailing
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(Original post by old_engineer)
To answer this question you probably have to assume that students' scores are normally distributed. You also have to guess whether the 95% of students means that 95% of students will score <= a particular score, or >= a particular score, or whether the 95% is supposed to be symmetrically arranged either side of the mean. I think the last of those options is most likely, in which case, the 5% of students not included in the central 95% will be divided equally between lower and upper tails of 2.5% each. What you then need to know is that, for a normal distribution, an upper tail of 2.5% starts 1.96 standard deviations above the mean, with similar reasoning for the lower tail. You will find these and similar % figures in a table of percentage points for the normal distribution, contained in textbooks and A level formula. booklets.
you could also use the ‘central’ function on the calculator that will figure out the values on either side for you i think ur way is also correct, but just v complicated haha
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anaindiemood
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(Original post by arwaisfailing)
try plugging in ur values into that inverse normal section and tell me what u do, and i’ll lyk if your answer matches mine
Hahhaa honestly the calculator confusion is making this a lot more complex than it needs to be I’m struggling🤣🤣
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arwaisfailing
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(Original post by anaindiemood)
Hahhaa honestly the calculator confusion is making this a lot more complex than it needs to be I’m struggling🤣🤣
aw okay, tell me what you know and what ur unsure about
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anaindiemood
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(Original post by arwaisfailing)
aw okay, tell me what you know and what ur unsure about
I’m just not really sure which values I’m meant to be typing in to each section of the calculator!
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arwaisfailing
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okay so,
data : variable (it’s always this)

tail: central (as the question does not say top 95% or bottom 95%, so you can assume it’s just the middle 95%)

area: 0.95 (says 95% in question)

standard deviation symbol: 13 (this is the square root of variance, so in this case, 13)

mean symbol: 108 (in question)

really hoping ur calculator looks similar to mine and this makes sense!
Last edited by arwaisfailing; 1 month ago
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anaindiemood
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(Original post by arwaisfailing)
okay so,
data : variable (it’s always this)

tail: central (as the question does not say top 95% or bottom 95%, so you can assume it’s just the middle 95%)

area: 0.95 (says 95% in question)

standard deviation symbol: 13 (this is the square root of variance, so in this case, 13)

mean symbol: 108 (in question)

really hoping ur calculator looks similar to mine and this makes sense!
When you first go on the calculator and select a mode is it the distribution mode?
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anaindiemood
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(Original post by arwaisfailing)
okay so,
data : variable (it’s always this)

tail: central (as the question does not say top 95% or bottom 95%, so you can assume it’s just the middle 95%)

area: 0.95 (says 95% in question)

standard deviation symbol: 13 (this is the square root of variance, so in this case, 13)

mean symbol: 108 (in question)

really hoping ur calculator looks similar to mine and this makes sense!
Ok I think I finally got it! Thanks so much for your help🥰🥰
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