Evaluating probability: A particular type of mouse's weights are normally distributed, with a mean of 726 grams and a standard deviation of 23 grams. If you pick one mouse at random, find the following: (round all probabilities to four decimal places) a) What is the probability that the mouse weighs less than 722 grams

0.4325 = 43.25% probability that the mouse weighs less than 722 grams

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 of 726 grams and a standard deviation of 23 grams.

This means that

a) What is the probability that the mouse weighs less than 722 grams

This is the p-value of Z when X = 722. So

has a p-value of 0.4325

0.4325 = 43.25% probability that the mouse weighs less than 722 grams

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.