Answered

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About 78% of all female heart transplant patients will survive at least 3 years. Eighty female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than 70%?. Assume the sampling distribution of sample proportion is a normal distribution. The mean of the sample proportion is equal to the population and the standard deviation is equal to square root of pq/n. The probability that the sample proportion surviving for at least 3 years will be less than 70% is _ . Round to 4 decimal places

Sagot :

In this case

[tex]p=0.78[/tex]

[tex]n=80[/tex][tex]np=62.4[/tex][tex]q=1-p=0.22[/tex][tex]nq=17.6[/tex][tex]\text{Mean}=0.78=0.78[/tex][tex]\text{StandarDeviation}=\sigma=\sqrt[]{\frac{0.78\cdot0.22}{80}}\approx0.04631[/tex]

And the probability that the sample proportion surviving for at least 3 years will be less than 70% is approximately 0.0421

The Z-score in this case is:

[tex]Z=\frac{0.78-0.7}{0.04631}=1.7273[/tex]

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