The time spent (in days) waiting for a heart transplant in two states for patien

Question

The time spent (in days) waiting for a heart transplant in two states for patients with type A^+ blood can be approximated by a normal distribution, as shown in the graph to the right. Complete parts and below. What is the shortest time spent waiting for a heart that would still place a patient in the top 20% of waiting times? days (Round to two decimal places as needed) What is the longest time spent waiting for a heart that would still place a patient in the bottom 10% of waiting times? days (Round to two decimal places as needed.)

Explanation / Answer

Solution:

mean = 122
SD = 20.6

looking up a z- table

(a) q1
z- value for top 20% waiting time = +0.8416
shortest time for top 20% waiting = mean + 0.8416*SD
= 124 + 20.6 *0.8416

= 141.34 => 141 days

(b) q2
z-value for bottom 1% waiting time = -1.2815
longest time for bottom 1% waiting = mean -1.2815 *SD
= 122 - 20.6 * 1.2815
= 95.60 => 95 days

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