Gavyn rolls a fair dice 540 times.<br> How many times would Gavyn expect to roll a four?

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

1 year ago

To determine what students at a school would be willing to do to help address global warming, researchers take a random sample o

erastovalidia [21]

Answer:

(ai) The correct answer is the first option; The amount of tax the student is willing to add to a gallon of gasoline.

(aii) The correct answer is the last option; Whether the student believes that global warming is a serious issue or not.

(b) The correct answer is the first option; two-sample t interval

Step-by-step explanation:

A response variable in statistics is the idea or concept of needs to be proven right or wrong. It remains a response variable until it has been proven.

An explanatory variable simply means an independent variable. It doesn't depend on any other variable and at the same time, it can be manipulated.

In construct a 95% confidence interval to compare the two groups, two-sample t test is the appropriate t test to use.

7 0

1 year ago

A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4

Natasha2012 [34]

Reflection on the -x axis

7 0

1 year ago

Read 2 more answers

A warehouse has boxes that are 18 inches tall and other boxes that are 30 inches tall. If 18 inch boxes is stacked next to 30 in

Aleksandr-060686 [28]

90 inches 18 times 5 is 90 and 30 times 3 is 90 so the lowest point which they will be at the height is 90 inches

4 0

2 years ago

One of the sides of a parallelogram is 4.2 cm and the altitude to that side is 3.6 cm. Find the perimeter of the parallelogram i

dexar [7]

Area of parallelogram = base * height
base 1 = 4.2 cm
height 1 = 3.6 cm
∴ Area = 4.2 * 3.6 = 15.12

let the other base 2 = x
∴ the altitude of this base = height 2 = 2.4
∴Area = 2.4 x = 15.12
Solve for x
∴ x = 6.3 cm

∴ The perimeter of parallelogram = 2( base 1 + base 2)
= 2 ( 4.2 + 6.3 ) = 21 cm

7 0

2 years ago

Gavyn rolls a fair dice 540 times. How many times would Gavyn expect to roll a four?