The difference between two numbers is 3. the sum of the two numbers is 21. what is the product of the two numbers

When Samuel commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 32 minutes and a

k0ka [10]

Answer:

$z=\frac{x-\mu}{\sigma}$

And we can find the nnumber of deviations from the mean for each limit given:

$z_1 = \frac{17-32}{5} = -3$

$z_2= \frac{47-32}{5} = 3$

So we are 3 deviation from the mean and using the empirical rule we know that within 3 deviations from the mean we have 99.7% of the values

Step-by-step explanation:

Let X the random variable that represent the amount of time it takes him to arrive, and for this case we know the distribution for X is given by:

$X \sim N(32,5)$

Where $\mu=32$ and $\sigma=5$

We want to find this probability:

$P(17$

And we can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

And we can find the nnumber of deviations from the mean for each limit given:

$z_1 = \frac{17-32}{5} = -3$

$z_2= \frac{47-32}{5} = 3$

So we are 3 deviation from the mean and using the empirical rule we know that within 3 deviations from the mean we have 99.7% of the values

8 0

3 years ago

Identify the pair of lines as parallel, perpendicular, or neither.

Mumz [18]

Answer:

Parallel

Step-by-step explanation:

The slopes are the same, they are both 0.

3 0

3 years ago

A television station plans to ask a random sample of 400 city residents if they can name the news anchor on the evening news at

hodyreva [135]

Answer:

There is an 8.38% probability that the anchor will be fired.

Step-by-step explanation:

For each resident, there is only two possible outcomes. Either they can name the news anchor on the evening news at their station, or they cannot.

This means that the binomial probability distribution will be used in our solution.

However, we are working with samples that are considerably big. So i am going to aaproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X), \sigma = \sqrt{V(X)}$ .