Answer:
(x² - 9)(x² - 2) = 0
x = 3 or √2
Step-by-step explanation:
To factor a polynomial, you need to find two expression that when multiplied together using FOIL (first, outside, inside, last) will produce the polynomial. In this case the polynomial can be factored into:
(x² - 9)(x² - 2) = 0
Setting each of these expressions equal to '0':
x² - 9 = 0 or x² = 9 so √x² = √9 or x = 3
x² - 2 = 0 or x² = 2 so √x² = √2 or x = √2
Answer:
a) 26.76% probability that a student in the psychology department has a score less than 480.
b) 69.73% probability that a student in the psychology department has a score between 480 and 730.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we haev that:
a. Find the probability that a student in the psychology department has a score less than 480.
This is the pvalue of Z when X = 480. So
has a pvalue of 0.2676.
26.76% probability that a student in the psychology department has a score less than 480.
b. Find the probability that a student in the psychology department has a score between 480 and 730.
This probability is the pvalue of Z when X = 730 subtracted by the pvalue of Z when X = 480.
X = 730
has a pvalue of 0.9649.
X = 480
has a pvalue of 0.2676.
0.9649 - 0.2676 = 0.6973
69.73% probability that a student in the psychology department has a score between 480 and 730.