The ime spent (in days) walting for a heart transplant in two states for patents

Question

The ime spent (in days) walting for a heart transplant in two states for patents with type A" blood can be approximated by a omal disribution asshown int graph to the right Complete parts(a) and (b) below Click to e page 2 of the tabli (a) What is tho shonest time spent waiting tor a heartthat would s place a paient inthe top 30% of wating tirres? days(Round to two doanal places as needed) (b) what is the longest ino spntl waligfo.lwa'that would sta plece a patient ine bottom 1% of waling.es? dwys(Round to his decimal places as needed)

Explanation / Answer

Solution:

We are given that the random variable X follows a normal distribution.

µ = 134

= 22.8

Part a

First of all we have to find the value of X for the upper 30% or lower 70% area.

Critical value for lower 70% area or upper 30% area is given as below:

Z = 0.524401

(By using z-table or excel)

X = µ + Z*

X = 134 + 0.524401*22.8

X = 145.96

Required Answer = 145.96

Part b

Here, we have to find X value for the bottom 1% area.

Critical value for bottom 1% area is given as below:

Z = -2.32635

X = µ + Z*

X = 134 + (-2.32635)*22.8

X = 134 - 2.32635*22.8

X = 80.95922

Required Answer = 80.96

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