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# In its standardized form, the normal distribution

1. In its standardized form, the normal distribution
a) has a mean of 0 and a standard deviation of 1.
b) has a mean of 1 and a variance of 0.
c) has an area equal to 0.5.
d) cannot be used to approximate discrete probability distributions.

2. For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770. Find value of Z?

3. For some value of Z, the probability that a standard normal variable is below Z is 0.2090. Find value of Z?

4. For some positive value of X, the probability that a standard normal variable is between 0 and +2X is 0.1255. Find value of X?

For 2,3,4 I need detail calculation and explanation.

#### Solution Preview

1. In its standardized form, the normal distribution
a) has a mean of 0 and a standard deviation of 1. < True
b) has a mean of 1 and a variance of 0.
c) has an area equal to 0.5.
d) cannot be used to approximate discrete probability distributions.

2. For some positive value of Z, the probability that a standard normal ...

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