Find the area under the standard normal curve for the following:
(A) P(z < -1.80)
(B) P(-1.93 < z < 0)
(C) P(-0.17 < z < 2.05)
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores.
To find the area under the standard normal curve, you can use a standard normal distribution table or a statistical calculator. The standard normal distribution table provides the area to the left of a given z-score.
(A) P(z < -1.80):
To find the area to the left of -1.80 on the standard normal curve, you need to consult the standard normal distribution table. Locate the row corresponding to -1.8 and find the corresponding column heading for the hundredths place of the z-score. The value in that cell represents the area to the left of -1.80.
(B) P(-1.93 < z < 0):
To find the area between -1.93 and 0, you need to find the area to the left of 0 and subtract the area to the left of -1.93. Again, consult the standard normal distribution table to find the area to the left of each z-score.
(C) P(-0.17 < z < 2.05):
Similarly, to find the area between -0.17 and 2.05, you need to find the area to the left of 2.05 and subtract the area to the left of -0.17.
Keep in mind that the standard normal distribution is symmetric, so finding the area to the left of a negative z-score is equivalent to finding the area to the right of the corresponding positive z-score.