Question 1:The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes, with the following results:

Arrivals Frequency

0 14

1 31

2 47

3 41

4 29

5 21

6 10

7 5

8 2

a. What is the probability that there will be fewer than two arrivals in a given minute?

b. What is the most probable number of arrivals per minute?

c. Determine the expected number of arrivals per minute.

d. Determine the variance and standard deviation of this distribution..

Question 2:The Internet has become a crucial marketing channel for business. According to a recent study, 91% of retail brands use two or more social media channels for business.

If a sample of 10 businesses is selected, what is the probability that:

a. 8 use two or more social media channels for business?

b. At least 8 use two or more social media channels for business?

c. At most 6 use two or more social media channels for business?

d. What is the expected value (mean) of this probability distribution?

Question 3:According to reports by interns to Glassdoor, the mean monthly pay for interns at Facebook is $6,589. Suppose that the intern monthly pay is normally distributed, with a standard deviation of $500. What is the probability that the monthly pay of an intern at Facebook is

a. less than $5,900?

b. between $5,700 and $6,100?

c. above $6,500?

d. Ninety-nine percent of the intern monthly pays are higher than what value?

e. Fifty percent of the intern monthly pays are between what two values, symmetrically distributed around the mean?