Statistics homework

Question

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 6.4 days and standard deviation of 1.1 days. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent.

a) What is the probability of spending less than 8 days in recovery?  % 

b) What is the probability of spending more than 4 days in recovery?  % 

c) What is the probability of spending between 4 days and 8 days in recovery?  % 

Answer 1

a) P(x<8) ?

s=1.1 x bar = 6.4, normally distributed

calculate the z score for 8

z = (8-6.4)/1.1 = 1.6/1.1 = 16/11 = about 1.45

find the area under the curve from z= 0 to 1.45

use z tables or a z calculator

then add .50 to get the proportion that are less then 8

multiply by 100 to get the percentage

b) P(x>4) = ?

calculate the z score for x=4

z= (4-6.4)/1.1 = -2.4/1.1 = about -2.27

find the area under the curve from z =-2.27 to 0

add .50

multiply by 100 to get the percentage

c) P(4<x<8) = ?

take the area under the curve from -2.27 to 0 and the area from 0 to 1.45 (from parts a and b above)

and add them

multiply by 100 to get the percentage