STATS - What is the shortest time spent waiting for a heart that would still place a patient in the top 10 percent of waiting times?
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.
(a) What is the shortest time spent waiting for a heart that would still place a patient in the top 10 percent of waiting times?
162.82 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 25 percent of waiting times?
117.39 days (Round to two decimal places as needed.)
Update:***How do I solve Parts A and B? I already have the answers but am clueless as to how to solve them. Thanks!
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a)
From the normal distribution table , P( z > 1.28 ) = 0.10
The top 10% point is 1.28
convert z to x
z = (x - μ) / σ
1.28 = (x - 133)/ 23.3
solve for x
(23.3)(1.28) = x-133
x= 133 + (23.3)(1.28) = 162.82 <----------
b)
From the normal distribution table , P( z < -0.67 ) = 0.25
The bottom 25% point is -0.67
convert z to x
z = (x - μ) / σ
-0.67 = (x - 133)/ 23.3
solve for x
(23.3)(-0.67) = x-133
x= 133 - (23.3)(0.67) = 117.39 <----------
What is the shortest time spent waiting for a heart that will place you in the top 20% mean 129 standard deviation 23.9