Question

A study in Batu Pahat General Hospital's on patient account division has compiled data on the age of accounts receivables. The data collected indicates that the age of the accounts follows a normal distribution with mean 28 days and standard deviation 8 days. Ahmad would like to know the probability of the accounts between 20 and 40 days old and the probability of the accounts which less than 30 days old. Shows the calculation of both problems.

Answer 1

Given :

Mean= 28

sd=28

To find :

We need to compute P(20≤X≤40). The corresponding z-values needed to be computed are:

$Z_1=\frac{X_1-mean}{sd}=\frac{20-28}{8}=-1$

$Z_2=\frac{X_2-mean}{sd}=\frac{40-28}{8}=1.5$

$=P(Z≤1.5)−P(Z≤−1)=0.9332−0.1587=0.7745$ (Using Z table )

Also We need to compute P(X<30). The corresponding z-value needed to be computed:

$Z= \frac{x-mean}{sd}= \frac{30-28}{8}=0.25$

Using Z table , P(Z<0.25)=0.5987