Using the standard normal distribution, find the probability that z is less than -1.78 (Points: 6)
0.0375
0.9625
0.9319
0.0384
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion that relates to that Z score. With a negative Z score, it will be either your first or fourth alternative.
.0375
To find the probability that z is less than -1.78 using the standard normal distribution, we can consult the z-table.
1. Locate the value -1.78 in the z-table.
2. The z-table provides the area under the curve to the left of a given z-value.
3. In this case, the area to the left of -1.78 is 0.0375.
Therefore, the correct answer is 0.0375.
To find the probability that a standard normal random variable is less than a given value, you can use a standard normal distribution table, also known as a z-table. The z-table provides the probability values for different z-scores.
To find the probability that z is less than -1.78, you need to look up the z-score -1.78 in the z-table.
The z-table is usually divided into positive z-scores, with the corresponding probabilities given in the body of the table. To find the probability for a negative z-score, you need to use the symmetry property of the standard normal distribution. Since the distribution is symmetric, the probability that z is less than -1.78 is equal to the probability that z is greater than 1.78.
Therefore, to find the probability that z is less than -1.78, we need to find the probability that z is greater than 1.78 in the z-table.
Looking up the z-score 1.78 in the z-table, we find the probability of 0.9625. Since we want the probability that z is less than -1.78, we subtract this value from 1 (since the total probability of the distribution is 1).
1 - 0.9625 = 0.0375.
Therefore, the probability that z is less than -1.78 is 0.0375.
So the correct answer is 0.0375.