What does 3m-3(m+8)>3m equal

Mathematics

2 answers:

Gelneren [198K]2 years ago

4 0

M < - 8 ..... <span>(3m - 3 • (m + 8)) - 3m > 0 </span>

Cloud [144]2 years ago

4 0

The answer is m < -8.

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For a fair coin, suppose you toss the coin 100 times.

Natasha_Volkova [10]

Using the normal distribution, it is found that there is a 0.0005 = 0.05% probability of getting more than 66 heads.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with $\mu = np, \sigma = \sqrt{np(1-p)}$ .

For the binomial distribution, the parameters are given as follows:

n = 100, p = 0.5.

Hence the mean and the standard deviation of the approximation are given as follows:

$\mu = np = 100(0.5) = 50$ .

$\sigma = \sqrt{np(1-p)} = \sqrt{100(0.5)(0.5)} = 5$

Using continuity correction, the probability of getting more than 66 heads is P(X > 66 + 0.5) = P(X > 66.5), which is <u>one subtracted by the p-value of Z when X = 66.5</u>.

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

$Z = \frac{66.5 - 50}{5}$