On average, the parts from a supplier have a mean of 31.8 inches and a standard deviation of 2.4 inches. Find the probability that a randomly selected part from this supplier will have a value between 27.0 and 36.6 inches. Is this consistent with the Empirical Rule of 68%-95%-99.7%?

The probability is P=0.9545.

The empirical rule is consistent, as it would have estimate a probability of 95%.

Step-by-step explanation:

We have a random variable with mean 31.8 in. and standard deviation of 2.4 in.

We have to find the probability that a randomly selected part from this supplier will have a value between 27.0 and 36.6 in.

If we assumed a normal-like distribution, we can calculate the z-score for both values:

That can be interpreted as an interval that is 2 standard deviations wide, centered on the mean.

This interval has a probability of:

If we apply the empirical rule, with 2 standard deviations from the mean, we would have estimate a probability of 95%, which is accurate.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

a is the right answer