Determine the are aunder the standard mnormal curve that lies to the left of
(a) Z= -1.68, (b) Z= -0.28,
(c) Z= -1.38, and (d) Z= 1.52
Find Z scores in table in back of your stats book labeled something like "area under normal curve".
Remember that "to the left" means values below that score. Also note that negative Z scores are below the mean.
Determine the area under the standard normal curve that lies between the following z scores. Use a table if necessary. Round your answer to four decimal places.
z = 0.36 and z = 1.93
To determine the area under the standard normal curve that lies to the left of a specific z-score, you can use a Z-table or a statistical calculator.
(a) Z = -1.68:
Using a Z-table or calculator, look up the area to the left of -1.68. The result is approximately 0.0465, or 4.65%.
(b) Z = -0.28:
Look up the area to the left of -0.28. This value is approximately 0.3897, or 38.97%.
(c) Z = -1.38:
Look up the area to the left of -1.38. This value is approximately 0.0838, or 8.38%.
(d) Z = 1.52:
Look up the area to the left of 1.52. This value is approximately 0.9357, or 93.57%.
Remember, the area to the left of a specific z-score represents the cumulative probability of observing a value less than that z-score in a standard normal distribution.
To determine the area under the standard normal curve that lies to the left of a given Z-score, we need to use a standard normal distribution table or a statistical calculator.
(a) Z = -1.68:
To find the area under the standard normal curve to the left of Z = -1.68, we can use a standard normal distribution table. The table provides the area to the left of a given Z-score.
Looking up the value of -1.68 in the table, we find that the area to the left of Z = -1.68 is approximately 0.0465 or 4.65%.
(b) Z = -0.28:
Using the same approach, we find the area to the left of Z = -0.28 from the standard normal distribution table. The table gives us the area to the left of a given Z-score.
Looking up the value of -0.28 in the table, we find that the area to the left of Z = -0.28 is approximately 0.3897 or 38.97%.
(c) Z = -1.38:
Again, using the standard normal distribution table, we can find the area to the left of Z = -1.38.
Looking up the value of -1.38 in the table, we find that the area to the left of Z = -1.38 is approximately 0.0838 or 8.38%.
(d) Z = 1.52:
Finally, we can find the area to the left of Z = 1.52 using the standard normal distribution table.
Looking up the value of 1.52 in the table, we find that the area to the left of Z = 1.52 is approximately 0.9357 or 93.57%.
Therefore, the areas under the standard normal curve that lie to the left of the given Z-scores are approximately:
(a) 4.65%
(b) 38.97%
(c) 8.38%
(d) 93.57%