Assume that females have pulse rates that are normally distributed with a mean of u = 75.0 beats per minute and a standard deviation of sigma = 12.5 beats per minute. If 1 adult female is randomly selected, find the probability that her pulse rate is between 69 beats per minute and 81 beats per minute.

36.88% probability that her pulse rate is between 69 beats per minute and 81 beats per minute.

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 the probability that her pulse rate is between 69 beats per minute and 81 beats per minute.

This is the pvalue of Z when X = 81 subtracted by the pvalue of Z when X = 69.

X = 81

has a pvalue of 0.6844

X = 69

has a pvalue of 0.3156

0.6844 - 0.3156 = 0.3688

36.88% probability that her pulse rate is between 69 beats per minute and 81 beats per minute.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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