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The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.9 days and a standard deviation of 2.5 days.

What is the 70th percentile for recovery times? (Round your answer to two decimal places.)

Respuesta :

LammettHash
The 70th percentile is the same as the cutoff recovery time [tex]t[/tex] such that every point above this time falls in the longest 30%, i.e.

[tex]\mathbb P(X>t)=0.30[/tex]

Transform to the standard normal distribution:

[tex]\mathbb P\left(\dfrac{X-5.9}{2.5}>\dfrac{t-5.9}{2.5}\right)=\mathbb P(Z>t^*)[/tex]

where [tex]t^*[/tex] is the z-score corresponding to the cutoff time [tex]t[/tex], which is approximately [tex]t^*\approx0.5244[/tex]. Solve for [tex]t[/tex]:

[tex]t^*\approx0.5244=\dfrac{t-5.9}{2.5}\implies t\approx7.21\text{ days}[/tex]

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