Question

For a standard normal distribution, given: P(z < c) = 0.469

Answer 1

P(Z<c)=0.469

We know that the probability, P(Z<c) indicates the area under standard normal curve to the left of x-axis value of Z=c (that is area under the curve for Z<c)

But the area under the standard normal curve to the left of mean (which is 0) is 0.5. But we have been given that the area under the curve to the left of c is only 0.469. This means the c is less than zero, that is c is negative.

So we rewrite the probability as

Now we can use the standard normal table

We know that a typical standard normal table lists the area only till the mean. That is to get the left tail probability we need to add 0.5 to the values listed.

So let us find the value of z for which we can get 0.531-0.5=0.031

the closest we can get to 0.031 is 0.0319. Hence we will use z=0.08. That is P(Z<0.08) = 0.5+0.0319=0.5319 which is close enough.

This means that P(Z<-0.08)=0.469 (which is what we want)

ans: c=-0.08