The magazine mass marketing company has received 10 entries in its latest sweepstakes. they know that the probability of receiving a magazine subscription order with an entry form is 0.5. what is the probability that more than two-fifths of the entry forms will include an order? round your answer to four decimal places.

P(X>4)= 0.624

Step-by-step explanation:

Given that

n = 10

p= 0.5 ,q= 1 - p = 0.5

Two fifth of 10 = 2/5 x 10 =4

It means that we have to find probability P(X>4).

P(X>4)= 1 -P(X=0)-P(X=1)-P(X=2)-P(X=3)-P(X=4)

We know that

P(X>4)= 1 -P(X=0)-P(X=1)-P(X=2)-P(X=3)-P(X=4)

P(X>4)= 1 -0.0009 - 0.0097 - 0.043 - 0.117-0.205

P(X>4)= 0.624

0.6231 = 62.31% probability that more than two-fifths of the entry forms will include an order

Step-by-step explanation:

For each entry, there are only two possible outcomes. Either there is a subscription order, or there is not. The probability of an entry having a subscription order is independent of other entries. So we use the binomial probability distribution to solve this quesiton.

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.

10 entries in its latest sweepstakes.

This means that n = 10.

They know that the probability of receiving a magazine subscription order with an entry form is 0.5.

This means that

What is the probability that more than two-fifths of the entry forms will include an order?

Two-fifths of 10 is 4. So

In which

0.6231 = 62.31% probability that more than two-fifths of the entry forms will include an order