Mathematics, 19.01.2021 19:40 adamske0

In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p? (a) n = 10, p = 0.5
(b) n = 40, p = 0.88
(c) n = 100, p = 0.2
(d) n = 100, p = 0.99
(e) n = 1000, p = 0.003

Answers: 1

Show answers

Answers

A Normal distribution to approximate probabilities for a binomial distribution with the given values of n = 100 and p = 0.2.

Given that,

Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p.

We have to determine,

In which of the following situations would it be appropriate to use a normal distribution to approximate probabilities for a binomial distribution with the given values of n and p.

According to the question,

Probabilities for a binomial distribution with the given values of n and p.

(a) n = 10, p = 0.5

(b) n = 40, p = 0.88

(d) n = 100, p = 0.99

(e) n = 1000, p = 0.003

To approximate to use the normal distribution for a binomial is given as,

$np\geq 10 , \ n(1-p)\geq 10$

When n = 10 and p = 0.5,

$= np \geq 10\\\\= 10 \times 0.5 = 5$

The normal distribution is less than 10 so, this not appropriate.

When n = 40 and p = 0.88,

$= n.p \geq 10\\\\= (40).(0.88) \geq 10\\\\= 35.2\geq 10\\\\Then,\\=n(1-p) = 40(1-0.88) \geq 10 \\\\= 40\times 0.12 \geq 10 = 4.8\leq 10$

The normal distribution is less than 10 so, this not appropriate.

When n = 100 and p =0.2,

$= n.p \geq 10\\\\= (100).(0.2) \geq 10\\\\= 20\geq 10\\\\Then,\\=n(1-p) = 100(1-0.2) \geq 10 \\\\= 100\times 0.8\geq 10 = 80\geq 10$

The normal distribution is greater than 10 so, this appropriate.

When n = 100 and p = 0.99,

$= n.p \geq 10\\\\= (100).(0.99) \geq 10\\\\= 99\geq 10\\\\Then,\\=n(1-p) = 100(1-0.99) \geq 10 \\\\= 100\times 0.01\geq 10 = 1\leq 10$

The normal distribution is less than 10 so, this not appropriate.

When n = 1000 and p = 0.003,

$= np \geq 10\\\\= 1000 \times 0.003 = 3$

The normal distribution is less than 10 so, this not appropriate.

Hence, A Normal distribution to approximate probabilities for a binomial distribution with the given values of n = 100 and p = 0.2.

To know more about Binomial Distribution click the link given below.

link

Answer from: jessicagustama

Step-by-step explanation:

To approximate to use the normal distribution for a binomial, we need that:

$np \geq 10, n(1-p)\geq 10$

So, for each option

(a) n = 10, p = 0.5

np = 10*0.5 = 5 < 10

So not appropriate

(b) n = 40, p = 0.88

np = 40*0.88 = 35.2 10

n(1-p) = 40*0.12 = 4.8 < 10

So not appropriate.

np = 100*0.2 = 20 10

n(1-p) = 100*0.8 = 80 10

So appropriate

(d) n = 100, p = 0.99

np = 100*0.99 = 99 10

n(1-p) = 100*0.01 = 1 < 10

So not appropriated

(e) n = 1000, p = 0.003

np = 1000*0.003 = 3 < 10

So not appropriate

Answer from: Quest

1.17+3.99a. you combine the terms with a to create 3.99 and the 1.17 stays because it has no like terms or a variable

Answer from: Quest

answer: 1722

step-by-step explanation:

given: the mass of saturn= $5.685\times10^{26}\ kgs$

the mass of mercury= $3.302\times10^{23}\ kgs$

the number of times the mass of saturn is greater than the mass of mercury

$=\frac{\text{mass of saturn}}{\text{mass of mercury}}\\=\frac{5.685\times10^{26}}{3.302\times10^{23}}\\\\=1.72168\times10^{26-23}{by using law of exponent}]\\=1.72168\times10^3=1721.68\approx1722$

hence, the mass of saturn is 1722 times greater than the mass of mercury.

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Which shows the correct lengths of side c in both scales? scale 1: 45 m; scale 2: 60 m scale 1: 60 m; scale 2: 45 m scale 1: 36 m; scale 2: 27 m scale 1: 27 m; scale 2: 36 m mark this and return save and exit

Answers: 3

Answer

Mathematics, 22.06.2019 00:30

Fixed rate mortgage offer: purchase price: $170,000 down payment ($34k): 20% term: 30 years interest rate: 4.25% property tax (yearly): $1,500 homeowner’s insurance (yearly): $1,000 use this example from a fixed-rate mortgage calculator to you answer the questions. keep the page open after you complete this question. according to the calculator, the monthly payment demarco and tanya should anticipate paying for principal and interest is $208. $877. $669. $1,200.

Answers: 1

Answer

Mathematics, 22.06.2019 00:30

(c) a vine called the mile-a-minute weed is known for growing at a very fast rate. it can grow up to 0.5 ft per day. how fast in inches per hour can the mile-a-minute weed grow up to? show your work using the correct conversion factors.

Answers: 1

Answer

Mathematics, 22.06.2019 01:00

The random variable x is defined as the number marking the sector in which the arrow lands when the spinner in the diagram is spun once.

Answers: 2

Answer

You know the right answer?

In which of the following situations would it be appropriate to use a Normal distribution to approxi...

Questions