The probability that the proportion surviving for at least five years
will exceed 80% is 0.00084
Step-by-step explanation:
The given is:
1. Suppose that 65% of all dialysis patients will survive for at least
5 years
2. A random sample has 100 new dialysis patients
We 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 = 0.04770
Now 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] = 3.14
Use 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%) = 0.00084
The probability that the proportion surviving for at least five years
will exceed 80% is 0.00084
Learn more:
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Answer:
0.00083
Step-by-step explanation:
In OLI Checkpoints, this is the answer it gave me in feedback.
