The probability that an appliance is in repair is 0.8. if an apartment complex has 100 such appliances, what is the probability that at least 90 will be in repair? use the normal approximation to the binomial.

Step-by-step explanation:

This situation can be modeled by a binomial distribution of parameters:

We want to find the probability that at least 90 are in repair.

We can approximate this problem to a normal distribution, where:

Then we look for

Then we must find the normal standard statistic Z-score

Therefore:

Looking in the standard normal table we obtain:

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b