Evan's new poetry collection will contain 55 poems. Evan can write poetry at a rate of two words a minute for a maximum of six hours each day. If each poem in Evan's collection contains an average of 213 words, how many days will it take Evan to finish the collection? (Round to the nearest whole number.)

4 days

Step-by-step explanation:

If there are 213 words in each poem, the the total number of words in all 55 poems will be 213 * 55 = 11715 words. He can also type two words per minute so using proportion,

If 2 words = 1 minute

11715 words = ?minutes

=

= 5857.5 minutes

Then we convert this into hours and then into days

60 mins = 1 hr

5857.5 mins = ?

=

= 97.625 hrs

24 hrs = 1 day

97.625 hrs = ?

=

= 4.07 days approximately 4 days

a)

b)

c)

d)

e)

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

Let X the random variable of interest, on this case we now that:

The probability mass function for the Binomial distribution is given as:

Where (nCx) means combinatory and it's given by this formula:

3) Part a

4) Part b

5) Part c

6) Part d

The expected value is:

7) Part e

The variance is given by: