Suppose that 65% of all dialysis patients will survive for at least 5 years. In a simple random sample of 100 new dialysis patients, what is the probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places?

The probability that the proportion surviving for at least five yearswill exceed 80% is 0.00084Step-by-step explanation:The given is:1. Suppose that 65% of all dialysis patients will survive for at least    5 years2. A random sample has 100 new dialysis patientsWe need to find the probability that the proportion surviving for at least five years will exceed 80%At first find σ from the rule below∵ σ = [tex]\sqrt{\frac{P(1-P)}{n}}[/tex]∵ P = 65% = 0.65∵ n = 100∴ σ = [tex]\sqrt{\frac{0.65(1-0.65)}{100}}[/tex]∴ σ = 0.04770Now find z-score from the rule:∵ z = (x - μ)/σ∵ x = 80% = 0.80∵ μ = P = 0.65∵ σ = 0.04770- Substitute these values in the rule∴ z = [tex]\frac{0.80-0.65}{0.04770}[/tex] = 3.14Use the normal distribution table for z-score to find the corresponding area of z = 3.14∵ The corresponding area is 0.99916∵ For P(x > 80%) the area to the right is needed∵ P(x > 80%) = 1 - 0.99916∴ P(x > 80%) = 0.00084The probability that the proportion surviving for at least five yearswill exceed 80% is 0.00084Learn more:You can learn more about the random sample in brainly.com/question/5510873 #LearnwithBrainly