Answer to Question #199698 in Statistics and Probability for kauser

Question

a) 10000 ‘Roshani’ light bulbs with a mean life of 150 days are installed in a new factory

and their length of life is normally distributed with standard deviation of 10 days.

How many Roshani-bulbs will expire in less than 160 days?

b) Plot the appropriate Graph. Here, objective is to show the linear relationship between

the sales of the product and amount spent in advertisement of a certain product.

 Based on the graphical output write your comment on linear association between these

two variables.

 Note: Participants may use MS-EXCEL, or they may prepare it on a piece of paper.

Region Sales(000'INR) Amount spent in Advertisement (000'INR)

1 260.3 5

2 286.1 7

3 279.4 6

4 410.8 9

5 438.2 12

6 315.3 8

7 565.1 11

Answer 1

a)

$z=\frac{x-\mu}{\sigma}=\frac{160-150}{10}=1.00$

$P(x<160)=P(z<1.00)=0.84134$

The number of bulbs that will expire in less than 160 days:

$n=10000\cdot0.84134=8413$

b)

We can conclude, that there is linear association on three intervals of the graph:

for $x\isin [5,8]$

for $x\isin [8,11]$

for $x\isin [11,12]$