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

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

(c) n = 100, p = 0.2

(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,

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

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

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

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

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

(c) n = 100, p = 0.2

Step-by-step explanation:

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

So, for each option

(a) n = 10, p = 0.5

So not appropriate

(b) n = 40, p = 0.88

So not appropriate.

(c) n = 100, p = 0.2

So appropriate

(d) n = 100, p = 0.99

So not appropriated

(e) n = 1000, p = 0.003

So not appropriate

it has the same slope and a different y-intercept

hope this : )