On Nov 5th 2021, the Minnesota Department of Health reported that 75% of Minnesotans (ages 16 and over) had received at least one dose of the COVID-19 vaccine. Using this proportion, answer the question below.

1. Suppose that I randomly select 10 Minnesotans (ages 16 and over). Using the binomial formula, find the probability exactly 8 of the 10 people selected have received the COVID-19 vaccine. Fill in the variables you will use and then calculate the probability. It is ok to check yourself using stat crunch, but please show your work with with the formula. Round to three decimal places.

p =

q =

n =

x =

Probability that exactly 8 of the 10 people have received the vaccine: ___________

1. Calculate the probability that at least 8Minnesotans in the sample of 10 have received the COVID-19 vaccine (this is a different question than number 1...do you see why? )

1. Using your answer from number 2, is it likely or unlikely that at least 8 Minnesotans (in a group of 10) have received the COVID-19 vaccine? (Remember we consider events with probabilities greater than 5% to be likely)

1. When using a binomial distribution, the mean (expected value) of the probability distribution is