Please help me ASAP!!!

A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at th

OlgaM077 [116]

Answer:

Interval [16.34 , 21.43]

Step-by-step explanation:

First step. Calculate the mean

$\bar X=\frac{(23+18+23+12+13+23)}{6}=18.666$

Second step. Calculate the standard deviation

$\sigma =\sqrt{\frac{(23-18.666)^2+(18-18.666)^2+(23-18.666)^2+(12-18.666)^2+(13-18.666)^2+(23-18.666)^2}{6}}$

$\sigma=\sqrt\frac{18.783+0.443+18.783+44.435+5.666+18.783}{6}$

$\sigma=\sqrt{17.815}=4.22$

As the number of data is less than 30, we must use the t-table to find the interval of confidence.

We have 6 observations, our level of confidence DF is then 6-1=5 and we want our area A to be 80% (0.08).

We must then choose t = 1.476 (see attachment)

Now, we use the formula that gives us the end points of the required interval

$\bar X \pm t\frac{\sigma}{\sqrt n}$

where n is the number of observations.

The extremes of the interval are then, rounded to the nearest hundreth, 16.34 and 21.43

6 0

3 years ago

A probability calculator is required on this problem; answer to six decimal places. Suppose we will spin the wheel pictured 400

KiRa [710]

Answer:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=400, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=400*0.2=80 \geq 10$

$n(1-p)=400*(1-0.2)=320 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=400*0.2=80$

$\sigma=\sqrt{np(1-p)}=\sqrt{400*0.2(1-0.2)}=8$

So then we can approximate the random variable as $X \sim N(\mu = 80, \sigma = 8)$

And we want this probability:

$P(90< X< 110)$

We can use the z score formula given by:

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

And replacing we got:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

8 0

3 years ago

What is the result of subtracting the polynomial (X2 + 3x) from the polynomial (-2X + 4X2 +5)?

HACTEHA [7]

Answer: -5x+3x²+5

Step-by-step explanation:

(-2x+4x²+5)-(x²+3x)

=-2x+4x²+5-x²-3x

=-2x-3x+4x²-x²+5

=-5x+3x²+5

=3x²-5x+5 (if you are required to write in standard form)

4 0

3 years ago

The first five terms of an arithmetic sequence are 8, 13/2, 5, 7/2, and 2. Which function, f(x), could be used to describe the x

juin [17]

Answer:

f(x) = 8 - 1.5x

Step-by-step explanation:

Here, we want to write a function that can be used to describe the x th term of the sequence

Mathematically, this can be calculated by looking at the numbers in the sequence

The difference between each successive term

is -1.5 ( 6.5-8, 3.5 -5)

So the formula for then x th term will be;

f(x) = 8 - 1.5x

where x refers to the number of the term , for example the 4th term

5 0

3 years ago

Read 2 more answers

A bag has five red stones two green three blue six yellow and four purple stones what is the probability of choosing a yellow st

Y_Kistochka [10]

Answer:

Probability of picking yellow stones from the bag is 0.3.

Step-by-step explanation:

Given:

Number of red stone in bag = 5

Number of green stone in bag = 2

Number of blue stone in bag = 3

Number of yellow stone in bag = 6

Number of purple stone in bag = 4

We need to find the probability of choosing yellow stone from the bag.

Solution:

First we will find the Total number of stones in the bag.

Total number of stones in the bag is equal to sum of Number of red stone in bag ,Number of green stone in bag, Number of blue stone in bag, Number of yellow stone in bag and Number of purple stone in bag.

framing in equation form we get;

Total number of stones in the bag = $5+2+3+6+4 =20$

Now Probability of picking yellow stones from the bag can be calculated by dividing Number of yellow stone in bag by Total number of stones in the bag.

framing in equation form we get;

$P(Y) =\frac{6}{20}= 0.3$

Hence Probability of picking yellow stones from the bag is 0.3.

4 0

3 years ago