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Sagot :
Given
mean = 3 days
standard deviation = 1.7 days
Find
a. What is the distribution of X?
b. What is the median recovery time?
c. What is the Z-score for a patient that took 4.1 days to recover?
d. What is the probability of spending more than 2.4 days in recovery?
e. What is the probability of spending between 2.7 and 3.4 days in recovery?
f. The 80th percentile for recovery times
Explanation
a) Distribution of X is given by X ~ N( 3 , 1.7)
b) for the normal distibution ,the median is the same as the mean .
so , the median recovery time is 3 days
c) z - score for the patient that took 4.1 days to recover is
[tex]\begin{gathered} z=\frac{X-\mu}{\sigma} \\ \\ z=\frac{4.1-3}{1.7} \\ \\ z=0.64705882352\approx0.6471 \end{gathered}[/tex]d) probability of spending more than 2.4 days in recovery
[tex]\begin{gathered} P(X>2.4)=P(\frac{X-\mu}{\sigma}>\frac{2.4-3}{1.7}) \\ \\ P(X>2.4)=P(Z>-0.3529) \\ P(X>2.4)=P(Z<0.3529) \\ \\ P(X>2.4)=0.6379 \end{gathered}[/tex]e) probability of spending between 2.7 and 3.4 days in recovery
[tex]\begin{gathered} P(2.7f) 80th percentile for recovery times = [tex]\begin{gathered} P(XFinal AnswerHence , the above are the required answers.
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