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

Question

The time spent(in days)waiting for a heart transplant in two states for patients with type blood can be approximated by a normal distribution, as shown in the graph to the right. Complete parts (a) and (b) below. (a) What is the shortest time spent waiting for a heart that would still place a patient in the top 15% of waiting times? days (Round to two decimal places as needed.) (b) What is the longest time spent waiting for a heart that would still place a patient in the bottom 1% of waiting times? days (Round to two decimal places as needed.)

Explanation / Answer

mean no days = 135

standard devaition = 20.7

a)

let the shortest time spent waiting for a heart that would still place in the top 15% of waiting times be T

P(X>=T) = 0.15 or 15%

P(X<T) = 1-P(X>=T) = 1-0.15 = 0.85

z value for T is (T-mean)/sd = (T-135)/20.7

z value for p=0.85 using z table is 1.0364

so (T-135)/20.7 = 1.0364

T = 135 +20.7*1.0364 = 156.45348 ~156.45

shortest time spent waiting for a heart that would still place in the top 15% of waiting times is 156.45

b)

let the longest time spent waiting for a heart that would still place in the bottom 1% of waiting times be T

P(X<=T) = 0.01 ot 1%

z value for T is (T-mean)/sd = (T-135)/20.7

z value for p=0.01 using z table is . -2.326348

so (T-135)/20.7 = -2.326348

T = 135 - 20.7*2.326348 = 86.8445964 ~ 86.84

longest time spent waiting for a heart that would still place in the bottom 1% of waiting times is 86.84

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