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

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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

both equations and proportions are better.

Answer from: Quest

1. 8

2. 9

3. 20

4. 3

5. 17

6. 2.2

7. 11.25

8. 1

9. 14

10. 2

step-by-step explanation:

thats the first half

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