Solve the system with substitution<br><br> 2.5x-3y=-13<br> 3.25x-y=-14

Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large un

spayn [35]

Answer:

60.26% probability that less than twenty students are absent

Step-by-step explanation:

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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 120, p = 0.15$ .

So

$\mu = E(X) = np = 120*0.15 = 18$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.15*0.85} = 3.91$

If a random sample of 120 names is called on a Monday, what is the probability that less than twenty students are absent?

This is the pvalue of Z when X = 20-1 = 19. So

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

$Z = \frac{19 - 18}{3.91}$

$Z = 0.26$

$Z = 0.26$ has a pvalue of 0.6026.

60.26% probability that less than twenty students are absent

3 0

3 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Archy [21]

Each quarter of a set of data is denoted by a quartile:

The 25th percentile makes up the first quartile Q1.
The 50th percentile represents the second quartile Q2.
The 75th percentile is the third quartile, or Q3.
Finding the second quartile, Q2, is simple. It divides an ordered data set into upper and lower half and is the median of any data set.

The median of the bottom half, excluding the value of Q2, makes up the first quartile, or Q1. The median of the upper half, excluding the value of Q2, makes up the third quartile, or Q3.

Sort the values in your data set from lowest to highest.
the median, please. Q2 stands for the second quartile.
Divide the ordered data collection in half at Q2.
The median of the lower half of the data makes up the lower quartile Q1.
The median of the data's upper half represents the upper quartile Q3.
When determining the first and third quartiles, omit the median if the size of the data set is unusual.
The median, if the size of the data collection is even, is the average of the middle two values. Add the two figures together, then divide by two. The value of the median, which divides the data set into lower and higher half, is

How to Find Interquartile Range
The interquartile range IQR is the range in values from the first quartile Q1 to the third quartile Q3. Find the IQR by subtracting Q1 from Q3.

IQR = Q3 - Q1

How to Find the Minimum

The minimum is the smallest value in a sample data set. Ordering a data set from lowest to highest value, x1 ≤ x2 ≤ x3 ≤ ... ≤ xn, the minimum is the smallest value x1. The formula for minimum is:

Min=1=min()=1

How to Find the Maximum

The maximum is the largest value in a sample data set.

Ordering a data set from lowest to highest value, x1 ≤ x2 ≤ x3 ≤ ... ≤ xn, the maximum is the largest value xn. The formula for maximum is:

Max==max()=1

How to Find the Range of a Set of Data

The range of a data set is the difference between the minimum and maximum. To find the range, calculate xn minus x1.

=−1

So to Answer your question

6 0

1 year ago

Hey can you please help me posted picture of question

True [87]

Ways to spot if an expression is not a polynomial:
1) If there is a negative exponent
2) If there is division by a variable
3) If the power is something other than a non-negative integer

If any of these conditions exist, the expression will not be a polynomial. Now consider the options. Option A has negative exponent, Option B involves division by a variable and Option D has a exponent which is not a number.

So, from the given options, option C is the only polynomial

7 0

3 years ago

What does this equal: 4 1/2 + 3 2/3=

professor190 [17]

4 1/2 + 3 2/3 = 8.16666667

8 0

3 years ago

Read 2 more answers

Question 10 of 25

vlabodo [156]

Answer:

0.5*13*15 = 97.5 square units

Step-by-step explanation:

If the diagonals of the rhombus are 13 and 15 then its area is 0.5*13*15 = 97.5 square units

8 0

3 years ago

Solve the system with substitution 2.5x-3y=-13 3.25x-y=-14