The patient recovery time from a surgical procedure is normally distributed with a mean of 6.3 days and a standard deviation of 5.1 days 1) What is the probability of spending more then two days in recovery? 2)  What is the 80th precentile for recovery items? Interpret in a sentence.

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The patient recovery time from a surgical procedure is normally distributed with a mean of 6.3 days and a standard deviation of 5.1 days

1) What is the probability of spending more then two days in recovery?

2)  What is the 80th precentile for recovery items? Interpret in a sentence.

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Step 1

The Z-score of a random variable X is defined as follows:

Z=(X–µ)/σ

Here, µ and σ are the mean and standard deviation of X, respectively.

Consider a random variable that defines the recovery time.

According to the given information X follows normal distribution with mean 6.3 days and standard deviation 5.1 days.

a)

The probability of spending more than two days in recovery is,

P(X>2)=P(Xµ)σ>(26.3)5.1 = 1-P(Z<-0.84) (Using Standard normal table: P(Z<-0.84)=0.2005)  =1-0.2005  =0.7995

Therefore, the probability of spending more than two days in recovery is 0.7995.

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