Assume that the random variable X is normally distributed with mean u = 45 and standard deviation o = 14.

Find P(57 < X < 69). Round to four decimal places

P(57 < X < 69) = 0.1513

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 have that:

Find P(57 < X < 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 0.9564

X = 57

has a pvalue of 0.8051

0.9564 - 0.8051 = 0.1513

P(57 < X < 69) = 0.1513

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step-by-step explanation:

pay attention in your classes and concentrate the best thing you can do to raise your test scores is to pay attention when you're supposed to be learning the material: in class!

take good notes.

do your homework.

use mnemonics and other tricks.

do practice tests.

note: the best i know.