this is a statistics problem

Question

P(x < 170) mean= 174 and the standard deviation = 20. I have to fine the indicated probability.

 

Answer 1

Calculate z-score: (170−174)÷20 gives -0.2.

Probability is given by (1/√(2π))∫_{(from z=-0.2 to z=0)}e^{(-z squared/2)}dz; this can be entered into a Casio Programmable Calculator as (1/√(2π))∑_{(from n=0 to n=∞)}(-1)ⁿz⁽²ⁿ⁺¹⁾÷[n!2ⁿ(2n+1)].

The calculator will compute a value of 0 for z=0 and a value of -0.07925970944 for z=-0.2.

Then 0−-0.07925970944 equals 0.07925970944.

Finally P(X<170) is given by 0.5−0.07925970944 equal to 0.4207402906 and equivalent to 0.4207.