Answer to Question #188229 in Statistics and Probability for lala

Question

1.    The mean number of hours a Filipino worker spends on the computer is 3.1 hr per workday. Assume the standard deviation is 0.5 hr and is normally distributed, how long does a worker spend on the computer if his z-score is 1.25?

2. Each month, a Filipino household generates an average of 28 pounds of

newspaper for garbage or recycling. Assume the standard deviation is 2

pounds. Determine the z-score of a household that generates 22 pounds

of newspaper

3. The Candelaria Automobile Association reports that the average time it

takes to respond to an emergency call is 30 minutes. Assume the variable

is normally distributed and the standard deviation is 45 minutes. How long

will a call be responded if it has a z-score of 0.75?

4. The average monthly salary for first-year teachers is P21,945. If the

distribution is approximately normal with a standard deviation of P3250.

How much will a teacher earn in a month if his salary has a z-score of

1.15?​

Answer 1

1.$\mu=3.1hrs, \sigma=0.5hrs, z=1.25$

 Then$x=\mu+z\times \sigma=3.1+1.25\times 0.5=3.725$ hrs

  

   Hence The worker spend 3.275hrs on the computer

2.The z score is-

  $=\dfrac{x-\mu}{\sigma}=\dfrac{22-28}{2}=-3$

3.$\mu=30 min, \sigma=45 min, z=0.75$

 Then $x=\mu+z\times \sigma=30+0.75\times 45=63.75 min$

 So, They respond after 63.75 min.

4.$\mu=21945,\sigma=3250,z=1.15$

  The amount teacher earn is 

     

   $x=\mu+z\times \sigma=21945+1.15\times 3250=25682.5$