Every 7 days a plant grows 4 centimeters. Complete the table.<br> 14 35 21 28

In a particular faculty 60% of students are men and 40% are women. In a random sample of 50 students what is the probability tha

zimovet [89]

Answer:

a) The expected value is given by:

$E(X) = np = 50*0.4 = 20$

and the variance is given by:

$Var(X) =np(1-p) = 50*0.4*(1-0.4) = 12$

b) $P(X>25)= 1-P(X\leq 25)$

And we can find this probability with the following Excel code:

=1-BINOM.DIST(25,50,0.4,TRUE)

And we got:

$P(X>25)= 1-P(X\leq 25)=0.0573$

c) 1) Random sample (assumed)

2) np= 50*0.4= 20 >10

n(1-p) =50*0.6= 30>10

3) Independence (assumed)

Since the 3 conditions are satisfied we can use the normal approximation:

$X \sim N(\mu = 20 , \sigma= 3.464)$

d) $P(X>25) = 1-P(Z< \frac{25-20}{3.464}) = 1-P(z$

e) $P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)$

$P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)= 1-P(Z$

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:

$X \sim Binom(n=50, p=0.4)$

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:

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

Part a

The expected value is given by:

$E(X) = np = 50*0.4 = 20$

and the variance is given by:

$Var(X) =np(1-p) = 50*0.4*(1-0.4) = 12$

Part b

For this case we want to find this probability:

$P(X>25)= 1-P(X\leq 25)$

And we can find this probability with the following Excel code:

=1-BINOM.DIST(25,50,0.4,TRUE)

And we got:

$P(X>25)= 1-P(X\leq 25)=0.0573$

Part c

1) Random sample (assumed)

2) np= 50*0.4= 20 >10

n(1-p) =50*0.6= 30>10

3) Independence (assumed)

Since the 3 conditions are satisfied we can use the normal approximation:

$X \sim N(\mu = 20 , \sigma= 3.464)$

Part d

We want this probability:

$P(X>25) = 1-P(Z< \frac{25-20}{3.464}) = 1-P(z$

Part e

For this case we use the continuity correction and we have this:

$P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)$

$P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)= 1-P(Z$

4 0

3 years ago

Find the sum.

Strike441 [17]

You are gonna use the distributive property.

4(2.5g - 4) + 3(1.2g - 2)

So you are going to multiply 4 with everything inside the first set of parenthesis and your gonna multiply 3 with everything insides the second set of parenthesis.

4 x 2.5g - 4 x 4 + 3 x 1.2g - 3 x 2

10g - 16 + 3.6g - 6

You wanna combine like terms:

10 - 3.6g + 16 - 6

6.4g + 10

You answer is 6.4g + 10.

Hope this Helps!!

6 0

2 years ago

A person invests 10000 dollars in a bank. The bank pays 4.5% interest compounded

Greeley [361]

The person would have to leave the money in the bank for 7.8 years for it to reach 13,500 dollars.

Step-by-step explanation:

Step 1; First we must calculate how much interest is generated for a single year. The annual interest rate is 4.5% i.e. 4.5% of 10,000 dollars which equals 0.045 × 10,000 = 450 dollars a year. As the years pass, more and more will be put into the account due to interest.

Step 2; For there to be 13,500 dollars in the bank account we need to calculate how much money is added due to interest.

The money needed to be added through interest = 13,500 - 10,000 = 3,500 dollars.

So we need to determine how long it will take for the bank to add 3,500 dollars by adding 450 dollars a year.

The number of years to reach 13,500 dollars = $\frac{3,500}{450}$ = 7.777 years. By rounding this value to the nearest tenth, we get 7.8 years.

7 0

2 years ago

Parallelogram or not ?

Zielflug [23.3K]

Answer:

I think so

Step-by-step explanation:

here's here's the definition of a parallelogram

"a four-sided plane rectilinear figure with opposite sides parallel."

3 0

2 years ago

Can i get some help thanks

inna [77]

Answer:

9300 maybe

Step-by-step explanation:

7 0

3 years ago

Every 7 days a plant grows 4 centimeters. Complete the table. 14 35 21 28