A level maths help

The continuous random variable X is normally distributed.
You are given that P(X less than178)=0.2659 and P(X greater than 187)=0.1914 .
Find the mean, , rounded to 1 dp.
2. Find the standard deviation, , rounded to 1 dp.

where are you stuck

you have to standardise using z

w


what do I put in the formula?

the formula is P(Z<x-mean/standard deviation)
so for example for p(x<178) you put p(z<178-mean/standard deviation)

then use inverse function on your calculator and set up simultaneous equations I think.

Thanks for your help but they haven't given the standard deviation in the question?

np, the point of standardising is so that you know the mean is 1 and the s.d. is 0. If you go on the inverse normal function on your calculator (for me its menu-7-3 you will see you can input an area mean and s.d. Since you will have standardised it you can say that for P(Z<178-mean/s.d) the area is .2659 and since you have standardised you can write s.d. as 1 and mean as 0. Press equals and I got -.625... Therefore you can say 178-mean/s.d is -.625 . Repeat this for the P(X>187) to get your 2 simultaneous equations involving two unknowns mean and s.d. then the rest is pretty straightforward. Hope this helped
P.S be careful when standardising P(X>187)=.1914, change this two P(X<187)=1-.1914 since the formula is for Z is less than then go from there.

np, the point of standardising is so that you know the mean is 1 and the s.d. is 0. If you go on the inverse normal function on your calculator (for me its menu-7-3 you will see you can input an area mean and s.d. Since you will have standardised it you can say that for P(Z<178-mean/s.d) the area is .2659 and since you have standardised you can write s.d. as 1 and mean as 0. Press equals and I got -.625... Therefore you can say 178-mean/s.d is -.625 . Repeat this for the P(X>187) to get your 2 simultaneous equations involving two unknowns mean and s.d. then the rest is pretty straightforward. Hope this helped
P.S be careful when standardising P(X>187)=.1914, change this two P(X<187)=1-.1914 since the formula is for Z is less than then go from there.

Hi so I did this and got 2 means. How do I set up the simultanoues equations for this?