1.) 5 patients qualify to have a surgical procedure performed. The doctor states that there is an 80% chance of a successful surgery. The random variable x represents a successful surgery. Find the following probabilities. Please set up your probabilities, show all steps for solving and use the equation editor to format your equations.

a.) Probability of exactly 3 successful surgeries.

b.) Probability of at least 3 successful surgeries.

c.)  Probability of more than 3 successful surgeries.

d.) Probability of fewer than 3 successful surgeries.

e.) Probability of no successful surgeries.

f.)   Probability of 5 successful surgeries.

2.) 5 patients qualify to have a surgical procedure performed. The doctor states that there is an 80% chance of a successful surgery. Answer the questions below. Please show all steps for solving and use the equation editor to format your equations.

a.) Calculate the mean, variance and standard deviation for the binomial probability distribution. Please show your steps and use the equation editor to format your answers.

Mean:

Variance:

Standard Deviation:

b.) Use the range rule of thumb to determine if it would it be considered unusual to have exactly 2 successful surgeries? Explain.

c.)  Based on your calculated statistics, if you needed to have the surgical procedure performed, would you choose this doctor? Explain.