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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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