Use Table A to find the proportion of observations from the standard Normal distribution that satisfies each of the following statements. In each case, sketch a standard Normal curve and shade the area under the curve that is the answer to the question. Use your calculator or the Normal Curve applet to check your answers.

More Table A practice

(a) $z$is between −$2.05$and $0.78$

(b) $z$is between −$1.11$and −$0.32$

It is given in the question that,

$z$is between $-2.05$and $0.78$

The below Standard Normal probabilities table is a table of areas under the standard Normal Curve. The table entry for each value $z$is the area under the curve to the left of $z$.

Shows the graph and table.

(a) A standard normal probability table shows the area to the left of$z=0.78$is $0.7823$and the area to the left of $z=-2.05$is $0.0202$.

Between $z=-2.05$and $z=0.78$there is a mass that is half of what is to the left of$0.78$minus the area to the left of $-2.05$.

Area between $z=-2.05\&z=0.78$ is:

$0.7823-0.0202=0.7621$

By the graphical representation , the result will be,

It is given in the question that,

z is between $-1.11$and $-0.32$

(b) A standard normal probability table shows that the area to the left of $z=-0.32$is $0.3745$and the area to the left of $z=-1.11$is $0.1335$.

Between $z=-1.11$and $z=-0.32$there is a mass that is half of what is to the left of $-0.32$minus the area to the left of $-1.11$.

Area between $z=-1.11\&z=-0.32$:

$0.3745-0.1335=0.2410$

By the graphical representation , the result will be,