Forums › Ask ACCA Tutor Forums › Ask the Tutor ACCA MA – FIA FMA › Mean, Standard deviation.

- This topic has 6 replies, 2 voices, and was last updated 10 months ago by John Moffat.

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- May 12, 2022 at 12:54 pm #655458
Hi Mr. Maffot,

I know i asked this question earlier and you provided an explanation (thanks for that).

But i just want to clarify something. You indicated that the mean in this question was 50. But Isn’t the mean between 70 and 90, 80? Please explain this to me.Q1.) The percentage probability that a student will score more than 90 marks in an accounting exam is 2.28%. The marks scored from the accounting exam follow a normal distribution with a mean score of 70.

What is the standard deviation for the distribution?

May 12, 2022 at 2:49 pm #655468No. The mean is 70 (and is given in the question).

The distribution is symmetrical about the mean and therefore the probability of being above 70 is 50% (and that is what I wrote in my previous reply).

Have you watched my free lectures on this?

May 12, 2022 at 3:17 pm #655474Oh okay. Now i understand. I have watched your lecture on this sir.

May 12, 2022 at 3:23 pm #655475I just have another question on the same topic.

Q.) The height of boys in a class follows a standard normal distribution with a mean height of 175cm and a standard deviation of 10cm

What is the probability of the boys being taller than 195cm?

I understand how to solve this question for the most part. But what i don’t understand is why we minus 0.5 and 0.4772. I know how to arrive at 0.4772 but why do we minus it from 0.5? If you could please explain why i would really appreciate it. Thank you.

May 13, 2022 at 8:13 am #655521It is the same reason as in your previous question.

Because the distribution is symmetrical about the mean, 50% or 0.5 must be above the mean of 175cm.

If 0.4772 and between 175 and 195, then the proportion above 195 must be 0.5 – 0.4772.

May 14, 2022 at 2:28 pm #655634I have one final question about this topic sir. How do you calculate the probability being 50%. Or how do you calculate the probability in general.

May 14, 2022 at 3:00 pm #655640Because the curve is symmetrical, the probability of being above or below the mean is 50% (or 0.5). Other probabilities are found using the normal distribution tables.

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