What is i^32? A.1 B. -1 C.-i D. i

We have n = 100 many random variables Xi ’s, where the Xi ’s are independent and identically distributed Bernoulli random variab

777dan777 [17]

Answer:

(a) The distribution of $X=\sum\limits^{n}_{i=1}{X_{i}}$ is a Binomial distribution.

(b) The sampling distribution of the sample mean will be approximately normal.

(c) The value of $P(\bar X>0.50)$ is 0.50.

Step-by-step explanation:

It is provided that random variables $X_{i}$ are independent and identically distributed Bernoulli random variables with p = 0.50.

The random sample selected is of size, n = 100.

(a)

Theorem:

Let $X_{1},\ X_{2},\ X_{3},...\ X_{n}$ be independent Bernoulli random variables, each with parameter p, then the sum of of thee random variables, $X=X_{1}+X_{2}+X_{3}...+X_{n}$ is a Binomial random variable with parameter n and p.

Thus, the distribution of $X=\sum\limits^{n}_{i=1}{X_{i}}$ is a Binomial distribution.

(b)

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

The sample size is large, i.e. n = 100 > 30.

So, the sampling distribution of the sample mean will be approximately normal.

The mean of the distribution of sample mean is given by,

$\mu_{\bar x}=\mu=p=0.50$

And the standard deviation of the distribution of sample mean is given by,

$\sigma_{\bar x}=\sqrt{\frac{\sigma^{2}}{n}}=\sqrt{\frac{p(1-p)}{n}}=0.05$

(c)

Compute the value of $P(\bar X>0.50)$ as follows:

$P(\bar X>0.50)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{0.50-0.50}{0.05})\\$

$=P(Z>0)\\=1-P(Z$

*Use a z-table.

Thus, the value of $P(\bar X>0.50)$ is 0.50.

8 0

3 years ago

Someone please help!! I’ll give brainliest:))

Allisa [31]

I’ve attached my work...
Hope it helps! Have a nice day :)

8 0

3 years ago

Lisa has played in six soccer matches. her brother Josh has played 18 soccer matches. Lisa says josh has played in 12 times as m

Tamiku [17]

Answer:

Josh has played in 3 times as many as Lisa has.

Step-by-step explanation:

She mixed up multiplication and addition.

6+12=18

6*3=18

6 0

3 years ago

Make 'y' the subject of the equation. x = 2y -7

geniusboy [140]

Answer:

y = (x + 7)/2

here's your solution

=>. it is given. x = 2y - 7

=> we have to make y as subject

=> now, we can writ this equation in this way

=> 2y - 7 = x

=> now put all constant to right side

=> 2y = x +7

=>. y = x+ 7 /2

hope it helps

5 0

2 years ago

How do you find the average rate change from x = -1 to x = 3

Marrrta [24]

Well to begin, you'll need a graph but you have to do:

y2-y1

---------

x2-x1

(Which is the average rate of change formula.)

In order to find your "y" you look for your x on the graph the move either direction until you touch the graph. Hope this helps.. :)

8 0

3 years ago