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# Normal Probability

1. For a standardized normal distribution calculate the following probabilities

a. P(0.00 < z < or equal to 2.33)
b. P( -1.00 < z < or equal to 1.00)
c. P( 1.78 < z < 2.34).

2. A random variable is normally distributed with mean of 25 and standard deviation of 5. If an observation is randomly selected

a. what value will exceed 10% of the time
b. What value will be exceeded 85% of the time
c. determine two values of which the smallest has 25% of the values below it and the largest value has 25% of the values below it and has 25% of the values above it.
d. what value will 15% of the observations be below.

3. A randomly selected value for a normal distribution is found to be 2.1 standard deviation above the mean.

a. what is the probability that a randomly selected value from the distribution will be greater than 2.1 standard deviation above the mean.
b. what is the probability that a randomly selected value from the distribution is less than 2.1 standard deviation from the mean.

#### Solution Summary

The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculation and Interpretations of the results are also included.

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