The weight of turkeys is normally distributed with a mean of 22 pounds and a standard deviation of 5 pounds. a. Find the probability that a randomly selected turkey weighs between 20 and 26 pounds. Your answer is . Round to 3 decimals and keep '0' before the decimal point. b. Find the probability that a randomly selected turkey weighs below 12 pounds. Your answer is . Round to 3 decimals and keep '0' before the decimal point.

a. 0.443

b. 0.023

Step-by-step explanation:

Problems of normal distributions can be 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.

The weight of turkeys is normally distributed with a mean of 22 pounds and a standard deviation of 5 pounds.

This means that

a. Find the probability that a randomly selected turkey weighs between 20 and 26 pounds.

This is the pvalue of Z when X = 26 subtracted by the pvalue of Z when X = 20. So

X = 26

has a pvalue of 0.788

X = 20

has a pvalue of 0.345

0.788 - 0.345 = 0.443

The answer is 0.443

b. Find the probability that a randomly selected turkey weighs below 12 pounds.

This is the pvalue of Z when X = 12. So

has a pvalue of 0.023

The answer is 0.023.

1 and 0

step-by-step explanation:

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.