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2 years ago

Discuss two other ways in which you encounter percentages in a typical week of your life

1 answer:

8 0

1) In school, you will encounter percentages on class assignments to see how much progress you made in an subject. 2) On a cell phone, you encounter percentages by how much your cell phone is charged in order to know if you need to charge the battery or not.

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Collect like terms to simply the expression

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In a particular class, there are 3 freshmen, 5 sophomores, 11 juniors, and 2 seniors. If the instructor randomly chooses a stude

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Freshmen/total
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1/7

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3 years ago

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The just-world hypothesis is ______. a. an ideology common in the United States that people get the outcomes they deserve b. a b

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The just-world phenomenon

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3 years ago

Kerry knit 16 winter hats to give as presents to her family. She wants to package the hats in gift boxes. She wants to put 5 hat

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she needs to buy 4 boxes since she can't buy a part of a box. assuming total boxes means completely filled boxes, then she fills 3

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2 years ago

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