given that X ~ N(m,5^2) and that P(X63) = 0.367 find m ? you are aloud to use a calculator but i dont know how to find m, without guess and check using a casio class pad calc. please help

Question

given that X ~ N(m,5^2) and that P(X>63) = 0.367 find m    ? you are aloud to use a calculator but i dont know how to find m, without guess and check using a casio class pad calc. please help

dumbcow · Answer

i will assume this is using the normal distribution where m is the mean and 25 is stnd dev ?

anonymous · Answer

yep you are correct exept 5 is the std deviation and 5^2 is the variance

dumbcow · Answer

oh ok...well you need to look up the Z-score
also note that most tables only give probabilities for "less than" so change it like this
P(X>63) = 1-P(X<=63) 
so look up 1-.367

then use z-score formula
$$Z = \frac{X-mean}{std dev}$$

anonymous · Answer

hmm what do you mean by 'most tables'?   and what would the X be?  1-0.367  ?

dumbcow · Answer

most stat textbooks provide standard normal probability tables to look up probabilities and z-scores... http://en.wikipedia.org/wiki/Standard_normal_table#Cumulative_table

anonymous · Answer

oh wow

dumbcow · Answer

X = 63
the probability of being less than 63 is (1-0.367)

anonymous · Answer

ohhh okay! i think i got ya thanks!

dumbcow · Answer

no problem :)

dumbcow · Answer

i get m = 61.3

anonymous · Answer

thats correct :)