Look at this set of ordered pairs:
(6, 4)
(9, 20)
(15, 15)
(12, 3)

Is this relation a function?

yes it is

Step-by-step explanation:

none of the x values are repeating in the pairs so it is considered a function. :)

0.8413 = 84.13% probability that a bolt has a length greater than 2.96 cm.

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 3 cm and a standard deviation of 0.04 cm.

This means that

What is the probability that a bolt has a length greater than 2.96 cm?

This is 1 subtracted by the p-value of Z when X = 2.96. So

has a p-value of 0.1587.

1 - 0.1587 = 0.8413

0.8413 = 84.13% probability that a bolt has a length greater than 2.96 cm.