It is believed to be true that 15% of the U.S. population is left-handed. You randomly select 8 people. Let r represent the number of left-handers.

1. Construct the binomial probability distribution. (Show 3 decimal places or as many as it takes to get to

one non-zero digit.) '

exactly 5 people are left-handed

less than 3 people are left-handed.

at least one person is left-handed

1. ) Find the mean and standard deviation of the binomial distribution. (Show/explain your work and use correct symbols for your answers. Round to the nearest hundredth, if applicable.)
2. Keep in mind that your book defines unusual as "more than 2.5 standard deviations from the mean". In a random sample of 7 people, would it be unusual to select 4 who are left-handed? __________ Show your work.
3. Using the table given in #1, fill in the blanks in the following sentence:
   1. In August 2021, the statistics class surveyed a TOTAL of _____ (n)students and found that _____ (r)were left-handed. (Use these answers for (b).)

1. (4 pts) Assuming that 15% of the population is left-handed, find the probability of surveying n students and getting exactly r"lefties". ________ (Round to 3 decimal places. Show or explain how you got the answer.)

r	p(r)