Question

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4 days and a standard deviation of 1.6 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N([],[])b. What is the median recovery time?daysc. What is the Z-score for a patient that took 5.7 days to recover? []d. What is the probability of spending more than 4.5 days in recovery? []e. What is the probability of spending between 3.5 and 4.3 days in recovery? []f. The 85th percentile for recovery times is []

Answer 1

Part B

What is the median recovery time?

Remember that

For a normal distribution, mean = median = mode

so

The median is 4 days

Part C

What is the Z-score for a patient that took 5.7 days to recover?

Remember that

z =(x - μ)/σ

where

μ=4 days

σ=1.6 days

X=5.7 days

substitute

z=(5.7-4)/1.6

z=1.0625

Part D

What is the probability of spending more than 4.5 days in recovery?

z =(x - μ)/σ

μ=4 days

σ=1.6 days

x=4.5 days

Find out z

z=(4.5-4)/1.6

z=0.3125

using a z-score table values

P(X>4.5)=0.3773

Part E

What is the probability of spending between 3.5 and 4.3 days in recovery?

For x=3.5 -------> z=(3.5-4)/1.6=-0.3125

For x=4.3 -----> z=(4.3-4)/1.6=0.1875

using a z-score table values

P(3.5 < X < 4.3)=0.1970

Part F

Remember that

If your score is in the 85th percentile, it means that 85% of the scores are below your score and 15% are above your score

using a z-score table values

the value of Z=1.036

Find out the value of x

1.036=(x-4)/1.6

solve for x

x=5.6576 days