A sample of size 126 will be drawn from a population with mean 26 and standard deviation 3. Use the TI-84 calculator. Part 1 Find the probability that x will be more than 25. Round the answer to at least four decimal places. The probability that x will be more than 25 is .
Part 2 Find the 55th percentile of x. Round the answer to two decimal places. The 55th percentile is .

1. The probability that x will be more than 25 is 0.6305.

2. The 55th percentile is 26.38.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score of a measure X is given by:

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.

Mean 26 and standard deviation 3.

This means that

1 Find the probability that x will be more than 25.

This is 1 subtracted by the p-value of Z when X = 25. So

has a p-value of 0.3695.

1 - 0.3695 = 0.6305.

The probability that x will be more than 25 is 0.6305.

2 Find the 55th percentile of x.

This is X when Z has a p-value of 0.55, so X when Z = 0.125.

The 55th percentile is 26.38.

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step-by-step explanation: