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# S1 normal distribution question watch

1. "A rival company Y sells bulbs with a mean lifetime of 860 hours and 20% of these bulbs have a lifetime of less than 818 hours.
(c) Find the standard deviation of the lifetimes of bulbs from company Y."

The mark scheme says that the z value equates to 0.8416 but can someone explain why this is so?
Because I drew out the diagram for it and since 20% of the bulbs have a lifetime of less than 818 hours, surely the Z value should equal a probability of z being less than 0.2 and in the normal distribution tables, this means that Z=0.4000.

0.8416 isn't even a probability in the tables, the closest one to it is 0.8413 and thats for when z=1. Argghhh I'm so confused!!!

(Btw I understand how to use the standardisation equation, I am just unsure why the z value that this equates to is 0.8416).
2. (Original post by jessyjellytot14)
"A rival company Y sells bulbs with a mean lifetime of 860 hours and 20% of these bulbs have a lifetime of less than 818 hours.
(c) Find the standard deviation of the lifetimes of bulbs from company Y."

The mark scheme says that the z value equates to 0.8416 but can someone explain why this is so?
Because I drew out the diagram for it and since 20% of the bulbs have a lifetime of less than 818 hours, surely the Z value should equal a probability of z being less than 0.2 and in the normal distribution tables, this means that Z=0.4000.

0.8416 isn't even a probability in the tables, the closest one to it is 0.8413 and thats for when z=1. Argghhh I'm so confused!!!

(Btw I understand how to use the standardisation equation, I am just unsure why the z value that this equates to is 0.8416).
It seems like you're looking at the wrong bits of the table.

You're right in that P(Z<z) = 0.2 for some z value that corresponds to a Y value (if we say Y~N(860, standard deviation^2)) so you need to find that z value and work your magic with the standardisation to find the thing you're looking for.

Which exam board are you with, by the way? Different boards have different tables and for Edexcel for example you can't directly read off P(Z<z) = 0.2
3. (Original post by jessyjellytot14)
"A rival company Y sells bulbs with a mean lifetime of 860 hours and 20% of these bulbs have a lifetime of less than 818 hours.
(c) Find the standard deviation of the lifetimes of bulbs from company Y."

The mark scheme says that the z value equates to 0.8416 but can someone explain why this is so?
Because I drew out the diagram for it and since 20% of the bulbs have a lifetime of less than 818 hours, surely the Z value should equal a probability of z being less than 0.2 and in the normal distribution tables, this means that Z=0.4000.

0.8416 isn't even a probability in the tables, the closest one to it is 0.8413 and thats for when z=1. Argghhh I'm so confused!!!

(Btw I understand how to use the standardisation equation, I am just unsure why the z value that this equates to is 0.8416).
So we want P(Z < z) = 0.2 Which is the same as saying P(Z> -z) = 0.2 - from which, the percentage points table lets you say that , the percentage points table is the table below the normal distribution table in your formula booklet.
4. (Original post by SeanFM)
It seems like you're looking at the wrong bits of the table.

You're right in that P(Z<z) = 0.2 for some z value that corresponds to a Y value (if we say Y~N(860, standard deviation^2)) so you need to find that z value and work your magic with the standardisation to find the thing you're looking for.

Which exam board are you with, by the way? Different boards have different tables and for Edexcel for example you can't directly read off P(Z<z) = 0.2
I'm doing Edexcel and I haven't seen the formula booklet yet, but in the textbook theres a whole page with the normal distribution table and then on the next page theres a percentage points table but I never know which one to use!

(Original post by Zacken)
So we want P(Z < z) = 0.2 Which is the same as saying P(Z> -z) = 0.2 - from which, the percentage points table lets you say that , the percentage points table is the table below the normal distribution table in your formula booklet.
Ohhh okay I see that now. But how do you know when to use the normal distribution table and when to use the percentage points table? Because 0.2 for example is on both tables, but each has a different value for it
5. (Original post by jessyjellytot14)

Ohhh okay I see that now. But how do you know when to use the normal distribution table and when to use the percentage points table? Because 0.2 for example is on both tables, but each has a different value for it
0.2 isn't in the normal table. The normal table starts from 0.5.
6. (Original post by jessyjellytot14)
I'm doing Edexcel and I haven't seen the formula booklet yet, but in the textbook theres a whole page with the normal distribution table and then on the next page theres a percentage points table but I never know which one to use!

Ohhh okay I see that now. But how do you know when to use the normal distribution table and when to use the percentage points table? Because 0.2 for example is on both tables, but each has a different value for it
0.2 is a probability (so a p or phi value) not a z value.
7. (Original post by tiny hobbit)
0.2 is a probability (so a p or phi value) not a z value.
(Original post by Zacken)
0.2 isn't in the normal table. The normal table starts from 0.5.
Ah I've been reading off the wrong columns
8. Well, by the central limit theorem: the sample means will be normally distributed.
QED
9. (Original post by BiggaQuestions)
Well, by the central limit theorem: the sample means will be normally distributed.
QED
Hilarious.

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