Question

assume the random variable X is normally distributed with mean u=50 and standard deviation of 7. What is the probability of P(X>35) and draw the curve.

Answer 1

we have given,

the random variable X is normally distributed with mean u=50 and standard deviation of 7.

let x ~normal distribution so we want to calculate p value from z score

so zscore is calculated by using formula

z =(x-mean)/sd

z = (x - )/

z = -2.142857

prob(x>35)=prob[(x - )/>35-50/7]

=prob(z> - 2.142857)

= 1 - prob(z<= - 2.142857)

=1- 0.016097 ( since prob(z<= - 2.142857)=0.016097 from z score table)

prob(x>35) =0.983903

probabity curve:-