I need some help with this ,a b and c

If the filling equipment is functioning properly what is the probability that the volume of oil in a randomly selected barrel wi

Sophie [7]

Answer:

$P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)$

$P(Z>0.8)=1-P(Z\leq 0.8)$

$P(Z>0.8)=1-0.788=0.212$

Step-by-step explanation:

Assuming this previous info : "Trucks carry barrels of crude oil from a port in Texas to a distributer in New Mexico on long trailers. Filling equipment is used to fill the barrels with the oil. When functioning properly, the actual volume of oil loaded into each barrel by the filling equipment at the port is approximately normally distributed with a mean of 55 gallons and a standard deviation of 0.5 gallons. If the mean is greater than 55.4 gallons, the filling mechanism is overfilling."

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the amount filling of a population, and for this case we know the distribution for X is given by:

$X \sim N(55,0.5)$

Where $\mu=55$ and $\sigma=0.5$

We are interested on this probability

$P(X>55.4)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)$

And we can find this probability using the complement rule:

$P(Z>0.8)=1-P(Z\leq 0.8)$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(Z>0.8)=1-0.788=0.212$

8 0

3 years ago

1. a. Maddy lost 18 pounds in 8 weeks. Find her rate of pounds lost per week.

Serjik [45]

Answer:

Step-by-step explanation:

2 and 1/4 lbs per week

5 0

3 years ago

1. If the amount of fruit decreased by 35%, what percent of the original amount do you have?

katovenus [111]

Answer:

65% of the original amount.

Explanation:

Let's say that the original amount is 100%; therefore, if we subtract 35% from the original amount we have

$100\%-35\%$ $=65\%$

Hence, if the amount of fruit decreased by 35%, then we have 65% of the original amount left.

6 0

2 years ago

Susan is making 8 casseroles. She uses 9 cans of beans. Each can is 16 oz. If she divides the beans equally among casseroles? Sh

belka [17]

Answer:

The correct answer will be 18

Step-by-step explanation:

First mutiply your object of the question which is 9 times 16 then make sure you have the right answer then divide it by 8 and 144 the answer you got, and you get 18

3 0

3 years ago

Wanda has $640 in her checking account. she pays her landlord $75 per week for rent.

Eddi Din [679]

The answer is y = 640 - 75x
As her balance starts at a fixed point ( 640)
and decrease every x weeks by 75
Hope it helps

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£( 'J')

4 0

3 years ago

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