- October 9, 2021 at 8:23 am #637288johnbrianeMember
- Topics: 170
- Replies: 160
sir this is a question from the acca site
the percentage probability that a student will score more than 90%in an accounting exam is 2.28%.
the marks scored from the accounting exam follow a standard normal distribution with a mean mark of 70%.
what is the standard deviation for the distribution ?
the answer is
the probability that a students mark is more than 90% is 2.28%
using the standard normal distribution table , work backwards to find
the z score .
Z = 0.50 – 0.0228 = 0.4772
so from the table = 2
z score = x – the mean / standard deviation
2 = 90 – 70 / std dev
so the answer is 10 which is the standard deviation .
according to my knowledge and as per what i learnt
It is simply a measure of the average spread of the distribution.
The lower the standard deviation then the less the spread is (if it is 0 then there is no
spread at all). The higher the standard deviation then the more the spread.
For example, suppose a data set has just two observations: 10 and 30. The
mean here is 20 and the standard deviation will be 10 as both observations are
10 units away from the mean.
so sir the problem i have is
in the above question the standard deviation was 10
but i cannot really understand what is the use of knowing this figure 10 ..
because the mean is 70
and then standard deviation is 10
is it something to do with knowing the below
“10 lower than 70 is 60 and 10 higher than 70 is 80”
sir i did watch the lectures and i do calculations very good but the theoratical part is lacking in meOctober 9, 2021 at 2:03 pm #637344John MoffatKeymaster
- Topics: 57
- Replies: 51543
The probability of being between the mean and 90% (which in this case is 47.72% or 0.4772) depends on how big the spread of the distribution is. If the spread is very small then the probability of being between the mean and 90% will be very high. If the spread is very large the the probability of being between the mean and 90% will be lower.
Since the standard deviation is measuring the spread, we look at the distance from the mean in numbers of standard deviations – i.e. the z-score.
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