Answer:
d. P(x = 0) = .50
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
a. P(x < 2) = .9772
This is the p-value of Z = 2.
Looking at the z-table, Z = 2 has a p-value of 0.9772, and thus, this probability is correct.
b. P(x ≥ 1) = .1587
This is 1 subtracted by the p-value of Z = 1.
Looking at the z-table, Z = 1 has a p-value of 0.8413.
1 - 0.8413 = 0.1587, and so, this probability is correct.
c. P(x ≤ 1) = .8413
This is the p-value of Z = 1, that is, 0.8413, so this is correct.
d. P(x = 0) = .50
The probability of an exact value on the normal distribution is 0, and thus, option d is wrong and is the answer to this question.
