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

Upper A Superscript plusA+

blood can be approximated by a normal distribution, as shown in the graph to the right. Complete parts (a) and (b) below.

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 (a) and (b) below. = 134 21.8 Click to view page 1 of the table 60 2100 (a) What is the shortest time spent waiting for a heart that would still place a patient in the top 10% 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 15% of waiting times? days (Round to two decimal places as needed.)

Explanation / Answer

Solution:

Normal Distribution
Mean ( ) =134
Standard Deviation ( sd ) = 21.8
Normal Distribution = Z= X- / sd ~ N(0,1)
a)
P ( Z > x ) = 0.10
Value of z to the cumulative probability of 0.15 from normal table is 1.28
P( x-u/ (s.d) > x - 134/21.8) = 0.10
That is, ( x - 134/21.8) = 1.28
--> x = 1.28 * 21.8+134 = 161.90400 ~ 161.90
b)
P ( Z < x ) = 0.15
Value of z to the cumulative probability of 0.01 from normal table is 1.04
P( x-u/s.d < x - 134/21.8 ) = 0.15
That is, ( x - 134/21.8 ) = 1.04
--> x = 1.04 * 21.8 + 134 = 156.67200 ~ 156.67

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