core assistance please

[tcstudent]

hi, this question may be easy for some but im really s..t..ruggling with this one lol

The length of a type of ant is approx normally distributed with a mean of 4.8mm and a standard deviation of 1.2mm

The standardised ant length of z= -0.5 corresponds to an actual ant length of

2.4
3.6
4.2
5.4 or 7.0

if someone knows the answer could they please tell me how not just give me the answer, thank you

[REBORN]

The appropiate formula here is: z = x-(xbar) over s where x = actual ant length, x bar = mean/average, s = standard deviation

-0.5 = (x-4.8 ) over 1.2

Solve using CAS or by hand

x = 4.2

[plato]

I think this type of question and calculation belongs in Methods but not in Further Maths where the only values of z are 0, 1, 2, 3 or -1, -2, -3 in reference to the 68-95-99,7% rule.

[b^3]

I think this type of question and calculation belongs in Methods but not in Further Maths where the only values of z are 0, 1, 2, 3 or -1, -2, -3 in reference to the 68-95-99,7% rule.

Nah this is pretty standard for a further question.

[brenden]

hi, this question may be easy for some but im really s..t..ruggling with this one lol

The length of a type of ant is approx normally distributed with a mean of 4.8mm and a standard deviation of 1.2mm

The standardised ant length of z= -0.5 corresponds to an actual ant length of

2.4
3.6
4.2
5.4 or 7.0

if someone knows the answer could they please tell me how not just give me the answer, thank you

I know the question has been answered, but just in case even having the formula still confuses the fuck out of you, I'll just explain the process I guess, I know not getting Further Math can be really frustrating sometimes... Sorry if I sound condescending lol, I'm not used to explaining math, so better be thorough, right?

Note that as soon as the question notes "normally distribution", you're dealing with a bell-curve. Or a 'normal distribution curve'. "standardised", "bell-shaped", "symmetrically distributed/symmetrical" are also words that should alert you to bell-cruve questions. What information do we have? 4.8 is the mean, so make a mental note that 4.8 lies down the dead centre of your bell curve... What else? 1.2 is the standard deviation. So, any value of a standard deviation just means that value lies between each percentile. So, between the mean and plus one standard deviations is 34%, right? So, one step to the right will be a value that is above the mean. But how much above the mean? This is standard deviation value. In this case, 1.2 is the standard deviation, which means that if we take one step to the right, 34% of people lie between the mean and 6.0 (because 4.8 + 1.2 = 6)
Now you need to take note that -0.5 is like a percentage of the standard deviation value. Any sort of z score will also work as a percentage of the standard deviation value. (By the way, this is just my way of thinking about it... don't worry if this doesn't make sense to you, because you'll find other ways)... The decimal 0.5 expressed as a percentage is what? 50%. So what's 50% of 1.2? It has to be 0.6, because 0.6 multiplied by two is 1.2. Pay close attention that the 0.5 is actually negative = -0.5
So, the length of the ant will be half of the standard deviation (1.2), subtracted from the mean value. This is because if we move half of one step to the left of our mean (half way to -1 standard deviations away from the mean), we only subtract half of the SD/Sx value from the mean value. So we get 4.2.

Sorry if that was entirely useless or annoying to read.

[tcstudent]

Thanks for your assitance guys, it will help me when it comes to exams because the question didnt come up in the CORE SAC i had this week, i scored 18/20 on the core sac, now im on too matrices module 6 so got to see how that is lol

[BubbleWrapMan]

Nah this is pretty standard for a further question.

Standard.

Hahahaha.