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djyliett [7]
3 years ago
13

Under what operations are the set of integers closed? Explain your answer.

Mathematics
1 answer:
Ostrovityanka [42]3 years ago
6 0
Integers are closed under addition, subtraction, and multiplication.Integers are not closed under division, For example, 1 divided by 3 is not an integer.
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The time for a visitor to read health instructions on a Web site is approximately normally distributed with a mean of 10 minutes
klio [65]

Answer:

a) The mean is 10 and the variance is 0.0625.

b) 0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.

c) 10.58 minutes.

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 establishes 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.

Normally distributed with a mean of 10 minutes and a standard deviation of 2 minutes.

This means that \mu = 10, \sigma = 2

Suppose 64 visitors independently view the site.

This means that n = 64,  = \frac{2}{\sqrt{64}} = 0.25

a. The expected value and the variance of the mean time of the visitors.

Using the Central Limit Theorem, mean of 10 and variance of (0.25)^2 = 0.0625.

b. The probability that the mean time of the visitors is within 15 seconds of 10 minutes.

15 seconds = 15/60 = 0.25 minutes, so between 9.75 and 10.25 seconds, which is the p-value of Z when X = 10.25 subtracted by the p-value of Z when X = 9.75.

X = 10.25

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

By the Central Limit Theorem

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

Z = \frac{10.25 - 10}{0.25}

Z = 1

Z = 1 has a p-value of 0.8413.

X = 9.75

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

Z = \frac{9.75 - 10}{0.25}

Z = -1

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826.

0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.

c. The value exceeded by the mean time of the visitors with probability 0.01.

The 100 - 1 = 99th percentile, which is X when Z has a p-value of 0.99, so X when Z = 2.327.

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

2.327 = \frac{X - 10}{0.25}

X - 10 = 2.327*0.25

X = 10.58

So 10.58 minutes.

6 0
2 years ago
A car travels 42 miles for every 2 gallons of gasoline. What is the unit rate?
svetoff [14.1K]

Answer:

21 miles per 1 gallon

Step-by-step explanation:

The unit rate is how many to 1 so, 42 divided by 2 equals 21 so, the answer is given.

PLZ MARK BRAINLIEST!!!

5 0
3 years ago
Read 2 more answers
Round 8.54 to the nearest tenth
olchik [2.2K]
The nearest tenth means 1 decimal place.
so the answer is 8.5
7 0
3 years ago
Read 2 more answers
A parabola has a vertex at (-6, 2) and opens down. Which of the following represents the
Setler [38]

Answer:

I don't see any choices but I think the axis of symmetry is x=-6.

Step-by-step explanation:

4 0
3 years ago
To qualify for gold status at awesome airlines, One must fly at least 16500 and less than 31500 miles each year. If Casey takes
SIZIF [17.4K]

Answer:

<em>[22,42]</em>

Step-by-step explanation:

<u>Division </u>

We must find an interval for the number of visits Casey needs to make to her parents to earn the gold status. The lower limit for that status is 16500 miles.

Each round trip flight Casey takes to visit her parents is 750 miles long. To know the minimum number of visits needed, we divide 16500 / 750= 22. To know the maximum number of visits, we divide 31500 / 750 = 42.

Thus, to earn the gold status at awesome airlines, Casey must go between 22 and 42 times to visit her parents. Expressing in interval notation: [22,42]

3 0
3 years ago
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