| Problem Statement |
P( X < A ) | P( X > A ) | P( A < X < B ) | P( X < A or X > B ) This assumes A<B. |
| Restatement using only < |
P( X < A ) | 1 - P( X < A ) | P( X < B ) – P( X < A ) | P( X < A ) + 1 - P( X < B ) |
| Standard Normal N( 0, 1 ) |
pnorm( A ) | 1 – pnorm(A) or pnorm( A, lower.tail=FALSE ) |
pnorm( B ) – pnorm( A ) | pnorm( A ) + ( 1 – pnorm( B ) ) or pnorm( A ) + pnorm( B, lower.tail=FALSE) |
| Non-Standard Normal N( C, D ) |
pnorm( A, mean=C, sd=D) | 1 – pnorm(A, mean=C, sd=D) or pnorm( A, mean=C, sd=D, lower.tail=FALSE ) |
pnorm( B, mean=C, sd=D ) – pnorm( A, mean=C, sd=D ) | pnorm( A, mean=C, sd=D ) + ( 1 – pnorm( B, mean=C, sd=D ) ) or pnorm( A, mean=C, sd=D ) + pnorm( B, mean=C, sd=D, lower.tail=FALSE) |
| Student's t with E degrees of freedom | pt( A, E) | 1 – pt(A, E) or pt( A, E, lower.tail=FALSE ) |
pt( B, E ) – pt( A, E ) | pt( A, E ) + ( 1 – pt( B, E ) ) or pt( A, E ) + pt( B, E, lower.tail=FALSE) |
| χ² with E degrees of freedom | pchisq( A, E) | 1 – pchisq(A, E) or pchisq( A, E, lower.tail=FALSE ) |
pchisq( B, E ) – pchisq( A, E ) | pchisq( A, E ) + ( 1 – pchisq( B ,E ) ) or pchisq( A, E ) + pt( B, E, lower.tail=FALSE) |