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Hi John Sorry I posted in PM instead
Hi John
Can you please help me with this question
The heights of adult females are normally distributed with a mean of 163 cm and a standard deviation
of 1.5 cm.
Ms X falls within one standard deviation of the mean. What range of heights does she fall
within?Answer is 161.5 – 164.5 cms
My working
1 SD = 0.3413
50 – 34.13 = 15.87%
z score of 15.87 % = 0.1554 & 0.1591
Average = 0.400 + 0.401 / 2 = 0.4005i’m stuck here. Can you kindly help
Please can you help with this too :
Based upon evidence from a number of years, PCM’s sales revenue is believed to be normally
distributed with a mean of $50,000 and a standard deviation of $8,000. The following
calculations have been used to illustrate what these signify:
I $50,000 + (1.65 × $8,000) = $63,200
II $50,000 – (1.65 × $8,000) = $36,800Answer
The probability that sales revenue will be in the range $36,800 to $63,200 is 90%.
The book doesn’t explain this and i tried calculating coefficient of variation but I dont think that is the way
First question:
Ms X will have a height between 1 SD below the mean of 163cm and 1 SD above the mean of 163cms.
1 SD 1.5cms, and therefore the heights are between 163 – 1.5 = 161.5, and 163 + 1.5 = 164.5 cms.
Second question:
For the probability to be 90%, there must be a probability of 45% of being above the mean of $50,000 and a 45% probability of being below the mean of $50,000.
Working backwards from the tables, for a probability of 0.45 (45%) the z score is 1.65.
The standard deviation is $8,000 and therefore 1.65 SD’s is 1.65 x $8,000.
Therefore there is a 90% probability of being between 1.65 x $8,000 below the mean and 1.65 x $8,000 above the mean.
Have you watched my free lectures on the normal distribution, because this is all explained in detail?
(I am puzzled as to why you are asking a question about Paper MA when you have also been asking questions about Paper AAA? You cannot have been taking Paper AAA without having already passed Paper MA. 🙂 )
Sorry John. I came across this in another qualification and your lecture for MA was really helpful. Thank you for all your help. You are truly changing people’s lives.
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