To determine the area under the standard normal curve that lies to the left of a given Z-score, we can refer to the table of areas under the normal curve.
(a) Z = -0.48:
To find the area to the left of Z = -0.48, we look up the Z-score in the table. The table provides the area between the mean (Z = 0) and the given Z-score. From the table, we find that the area to the left of Z = -0.48 is approximately 0.3159 (rounded to four decimal places).
Therefore, the area to the left of Z = -0.48 is approximately 0.3159.
(b) Z = 1.48:
To find the area to the left of Z = 1.48, we again look up the Z-score in the table. The table provides the area between the mean (Z = 0) and the given Z-score. From the table, we find that the area to the left of Z = 1.48 is approximately 0.9292 (rounded to four decimal places).
Therefore, the area to the left of Z = 1.48 is approximately 0.9292.
(c) Z = -1.37:
To find the area to the left of Z = -1.37, we refer to the table. The table gives us the area between the mean (Z = 0) and the given Z-score. From the table, we find that the area to the left of Z = -1.37 is approximately 0.0853 (rounded to four decimal places).
Therefore, the area to the left of Z = -1.37 is approximately 0.0853.
(d) Z = 1.59:
To find the area to the left of Z = 1.59, we use the table. The table provides the area between the mean (Z = 0) and the given Z-score. From the table, we find that the area to the left of Z = 1.59 is approximately 0.9441 (rounded to four decimal places).
Therefore, the area to the left of Z = 1.59 is approximately 0.9441.
In summary:
(a) The area to the left of Z = -0.48 is approximately 0.3159.
(b) The area to the left of Z = 1.48 is approximately 0.9292.
(c) The area to the left of Z = -1.37 is approximately 0.0853.
(d) The area to the left of Z = 1.59 is approximately 0.9441.