Let the probability of success on a Bernoulli trial be 0.30.
In five Bernoulli trials, what is the probability that there will be more than the expected number of failures? (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

0.4718 = 47.18% probability that there will be more than the expected number of failures.

Step-by-step explanation:

The binomial probability distribution is a sequence of Bernoulli trials.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

The expected value of the binomial distribution is:

In this problem we have that:

Let the probability of success on a Bernoulli trial be 0.30. Five Bernoulli trials. This means that

In five Bernoulli trials, what is the probability that there will be more than the expected number of failures?

The expected number of failures is:

So, either there are less than 1.5 failures, or there are more than 1.5 failures. The sum of the probabilities of these events is decimal 1. So

The number of failures is a discrete number, so

and

So

We want to find

So

In which

So

Rounded to four decimal places

0.4718 = 47.18% probability that there will be more than the expected number of failures.

d.) 48 units

step-by-step explanation: