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Dmitry [639]
3 years ago
12

According to the Sleep Foundation, the average night's sleep is 6.8 hours (Fortune, March 20, 2006). Assume the standard deviati

on is .4 hours and that the probability distribution is normal. What is the probability that a randomly selected person sleeps more than 8 hours (to 4 decimals)? What is the probability that a randomly selected person sleeps 6 hours or less (to 4 decimals)? Doctors suggest getting between 7 and 9 hours of sleep each night. What percentage of the population gets this much sleep (to the nearest whole number)?
Mathematics
1 answer:
vivado [14]3 years ago
5 0

Let X be the random variable for the time a given person from the population spends sleeping. With X\sim\mathcal N(6.8,0.4^2) we have

P(X>8)=P\left(\dfrac{X-6.8}{0.4}>\dfrac{8-6.8}{0.4}\right)=P(Z>3)\approx0.0013

where Z\sim\mathcal N(0,1^2).

P(X\le6)=P\left(\dfrac{X-6.8}{0.4}\le\dfrac{6-6.8}{0.4}\right)=P(Z\le-2)\approx0.0228

P(7

Rounded to the nearest whole number, that comes out to about 31%.

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A CBS News/New York Times opinion poll asked 1,190 adults whether they would prefer balancing the federal budget over cutting ta
nikklg [1K]

Using the <u>normal distribution and the central limit theorem</u>, it is found that there is a 0.0166 = 1.66% probability of a sample proportion of 0.59 or less.

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

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

  • It 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, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sampling proportions of a proportion p in a sample of size n has mean \mu = p and standard error s = \sqrt{\frac{p(1 - p)}{n}}

In this problem:

  • 1,190 adults were asked, hence n = 1190
  • In fact 62% of all adults favor balancing the budget over cutting taxes, hence p = 0.62.

The mean and the standard error are given by:

\mu = p = 0.62

s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.62(0.38)}{1190}} = 0.0141

The probability of a sample proportion of 0.59 or less is the <u>p-value of Z when X = 0.59</u>, hence:

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

By the Central Limit Theorem

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

Z = \frac{0.59 - 0.62}{0.0141}

Z = -2.13

Z = -2.13 has a p-value of 0.0166.

0.0166 = 1.66% probability of a sample proportion of 0.59 or less.

You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213

7 0
2 years ago
Will give brainliest!!
Inessa05 [86]
It’s actually B Bc the little 1 by the 10 is meaning that you are gonna multiply 10x10 one time. Then multiply by 7. 10x10=100 100x7=700 so there for your answer is B
4 0
3 years ago
Answer it answer it answer it
Usimov [2.4K]

Answer:

The correct option is;

C. 52.2 × 4.4 × 2 + 47.8 × 4.4 × 2

Step-by-step explanation:

The area of the square frame is the area of the inner square subtracted from the area of the outer square

Which gives;

52.2² - 47.8² = 440

Therefore;

Option A. 52.2² - 47.8² is a correct way of finding the area of the square frame

Option B. 2 × ((52.2×2.2) + (47.8×2.2)) = 440, is  a correct way of finding the area of the square frame

Option C. 52.2 × 4.4 × 2 + 47.8 × 4.4 × 2 = 880, is not a correct way of finding the area of the square frame

The error is the thickness is 2.2 not 4.4

Option D. 100×(52.2 - 47.8) = (52.2 + 47.8) × (52.2 - 47.8) = 52.2² - 47.8² = 440,  is  a correct way of finding the area of the square frame

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This is how you find the equation for the line

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