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klemol [59]
2 years ago
8

Geometry help thank you

Mathematics
1 answer:
Zanzabum2 years ago
4 0
Can't see the question that is being ask
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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
Suppose that an individual has a body fat percentage of 16.7% and weighs 188 pounds. How many pounds of his weight is made up of
Volgvan

Answer:

15.867

lbs or almost  

16

lbs.

Step-by-step explanation:

5 0
3 years ago
Which equation has 1 solution?<br><br> IwI = -2<br> IwI = -1<br> IwI = 0<br> IwI = - 1
vovangra [49]
Absolute value is alwas positive
so all of them excet the 3rd one are false

|w|=0 has 1 solution


if the last one was |w|=1 then ther would be 2 solutions, -1 and 1


answer is |w|=0
6 0
2 years ago
What is the value of x enter your answer in the box
OverLord2011 [107]

Answer:

x = 55°

Step-by-step explanation:

The sum of the 3 angles in a triangle is 180°

Subtract the sum of the 2 given angles from 180 for x

x = 180° - (75 + 50)° = 180° - 125° = 55°

6 0
3 years ago
Read 2 more answers
D= 2 - 6c <br> 1%2c - c = 1
omeli [17]
V????????????????????????????????????????????????????????????????13
3 0
3 years ago
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