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2 years ago

Rob needs to mix 4.5 liters of liquid fruit punch concentrate with 0.5

1 answer:

7 0

4.5 litres of fruit punch with 0.5 litres of water.
13.5 /4.5 = 3. Multiply 0.5 by 3 to get 1.5 litres of water. Therefore, 13.5 litres of fruit punch concentrate needs 1.5 litres of water. 13.5 + 1.5 = 15 litres of fruit punch in total.

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Engineers want to design seats in commercial aircraft so that they are wide enough to fit 95%of all males. (Accommodating 100%

Anarel [89]

Answer:

Upper P95 = 16.21in

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question, we have that:

$\mu = 14.4, \sigma = 1.1$

Upper P 95

This is the 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.

Then

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

$1.645 = \frac{X - 14.4}{1.1}$

$X - 14.4 = 1.1*1.645$

$X = 16.21$

Upper P95 = 16.21in

3 0

3 years ago

Find the 95% confidence interval for estimating the population mean μ

AVprozaik [17]

We first need to determine whether we are dealing with means or proportions in this problem. Since we are given the sample and population mean, we know that we are dealing with means.

Since we have one sample mean, this means we are creating a confidence interval for one sample (1 Samp T Int).

Normally we would check for conditions, but since this is not formulated as a "real-world scenario" type problem, it is hard to check for randomness and independence. Therefore, I will be excluding conditions from this answer.

<h3>Confidence Interval Formula</h3>

The formula for constructing a <u>confidence interval for means</u> is as follows:

$\displaystyle \overline{x} \pm t^*\big{(}\frac{\sigma}{\sqrt{n} } \big{)}$

We are given these variables:

$\overline{x}=50$
$n=60$
$\sigma=10$

Plug these values into the formula for the confidence interval:

$\displaystyle 50\pm t^* \big{(}\frac{10}{\sqrt{60} } \big{)}$

<h3>Finding the Critical Value (t*)</h3>

In order to find t*, we can use this formula:

$\displaystyle \frac{1-C}{2}=A$

Calculating the z-score associated with "A" will give us t*.

So, let's plug in the confidence interval 95% (.95) into the formula:

$\displaystyle \frac{1-.95}{2}=.025$

Use your calculator or a t-table to find the z-score associated with this area under the curve.. you should get:

$t^*=1.96$

<h3>Constructing Confidence Interval</h3>

Now, let's finish the confidence interval we created:

$\displaystyle 50\pm 1.96 \big{(}\frac{10}{\sqrt{60} } \big{)}$

We can calculate the confidence interval, using this formula, to be:

$\boxed{(47.4697, \ 52.5303)}$

<h3>Interpreting the Confidence Interval</h3>

We are 95% confident that the true population mean μ lies between <u>47.4697 and 52.5303</u>.

8 0

2 years ago

What are the like terms on the left side of the equation?

Dennis_Churaev [7]

Step-by-step explanation:

Like Terms: Terms that have identical variable parts (same variable(s) and same exponent(s)). When simplifying using addition and subtraction, you combine “like terms” by keeping the "like term" and adding or subtracting the numerical coefficients.

3 0

3 years ago

Read 2 more answers

Arrange the numbers in decreasing order 439.216,439.126,439.612,439.261

Free_Kalibri [48]

In decreasing order:

439.612, 439.261, 439.216, 439.126

8 0

3 years ago

Complementary events must have a sum of 1.

Bas_tet [7]

This is a true statement.

Consider two events A and B. We say they are complementary if P(A)+P(B) = 1

This means that either event A or event B must happen, since the "1" represents 100% probability. Having a probability of 100% means absolute certainty.

---------

Example:

A = the event it rains

B = the event it does not rain

P(A) = 0.30 = 30% chance of rain

P(B) = 0.70 = 70% chance it does not rain

P(A)+P(B) = 0.30+0.70 = 1

So this shows the two events are complementary.

8 0

3 years ago