Question

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4 days and a standard deviation of 1.7 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.

e. What is the probability of spending between 5 and 5.7 days in recovery?

f. The 80th percentile for recovery times is ____days.

Answer 1

Solution :

Given that ,

mean = = 4

standard deviation = = 1.7

e) P( 5 < x < 5.7) = P[(5 - 4)/ 1.7 ) < (x - ) /  < (5.7 - 4) / 1.7) ]

= P( 0.59 < z < 1.00 )

= P(z < 1.00 ) - P(z < 0.59)

Using z table,

= 0.8413 - 0.7224

= 0.1189

f) Using standard normal table,

P(Z < z) = 80%

= P(Z < z ) = 0.80

= P(Z < 0.84 ) = 0.80  

z = 0.84

Using z-score formula,

x = z * +

x = 0.84 * 1.7 + 4

x = 5.4 days