Assume that the random variable X is normally distributed, with mean muequals45 and standard deviation sigmaequals10. Compute the probability P(57 > than X less than or = 69).

0.1069 = 10.69%

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 question:

Between 57 and 69

This is the pvalue of Z when X = 69 subtracted by the pvalue of Z when X = 57. So

X = 69

has a pvalue of 0.9918

X = 57

has a pvalue of 0.8849

0.9918 - 0.8849 = 0.1069 = 10.69%

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation:

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