For this case we have the following equation:
Rewriting we have:
For expressions to be equal, exponents must be equal. So:
To factor, we look for two numbers that, when multiplied, result in -3 and when added, result in -2. These numbers are -3 and 1.
Thus, the roots are:
Answer:
Answer:
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.