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N76 [4]
3 years ago
6

Explain one relationship between capacity and fluid ounces

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
6 0
Capacity is the maximum amount that something can contain
fluid ounces is how much something contains in ounces.
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The Office of Student Services at a large western state university maintains information on the study habits of its full-time st
Vera_Pavlovna [14]

Answer:

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 20 hours, standard deviation of 6:

This means that \mu = 20, \sigma = 6

Sample of 150:

This means that n = 150, s = \frac{6}{\sqrt{150}}

What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.5. So

X = 21

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{21 - 20}{\frac{6}{\sqrt{150}}}

Z = 2.04

Z = 2.04 has a p-value of 0.9793

X = 19.5

Z = \frac{X - \mu}{s}

Z = \frac{19.5 - 20}{\frac{6}{\sqrt{150}}}

Z = -1.02

Z = -1.02 has a p-value of 0.1539

0.9793 - 0.1539 = 0.8254

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

3 0
3 years ago
Express number 9 as a unit rate, you can also round
Katena32 [7]
125/200= 0.625 cents

0.625 cents to the nearest cent= 0.63

The unit rate is 0.63 miles.

Hope this helps!







6 0
3 years ago
AB is 16 centimeters long. It is rotated 24° clockwise around point A. What is the length of the resulting line segment?​
makvit [3.9K]

Answer:

Step-by-step explanation:

4 0
2 years ago
How many like terms are in the expression:5a^2+6b+a^2-3b-2+4c.
Goryan [66]

Solution

Part 3

For this case we have 6 different terms

Part 4

We can do the following:

5a^2+a^2+6b-3b+4c-2

Part 5

And we can simplify on this way:

6a^2+3b+4c-2

7 0
1 year ago
Find the distance traveled by a car moving at an average<br> speed of 40 miles per hour 3 hours.
Grace [21]
Answer: 120 miles traveled
6 0
3 years ago
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