Question

6. Imagine that a soda bottling machine fills 550 ml bottles with a standard deviation of 7 ml. If we took 100 sample bottles, estimate how many bottles would meet the quality standard of selling bottles with at least 548ml

7. From the previous example, estimate the 70th decile of bottles and how many ml they would have of soda. That is, 70% of the bottles with more soda.

Answer 1

Solution :

Given that ,

mean = = 550 ml

standard deviation = = 7 ml

n = 100

6) P(x 548) = 1 - P(x   548)

= 1 - P[(x - ) / (548 - 550) / 7]

= 1 -  P(z -0.29)   

  Using z table,

= 1 - 0.3859

= 0.6141

7) Using standard normal table,

P(Z > z) = 70%

= 1 - P(Z < z) = 0.70  

= P(Z < z) = 1 - 0.70

= P(Z < z ) = 0.30

= P(Z < -0.52) = 0.30  

z = - 0.52

Using z-score formula,

x = z * +

x = -0.52 * 7 + 550

x = 546.36 ml