Question

Big Red soda is the "Faygo" of Texas. A local Texas grocery chain called H-E-B carries both name-brand Big Red soda and their store-brand equivalent called Wild Red soda. It is known that the sugar content of Big Red 20 ounce bottles is normally distributed with a mean of 63 g and a standard deviation of 1.1 g. It is also known that the sugar content of Wild Red 20 ounce bottles is normally distrbuted with a mean of 68 g and a standard deviation of 2.3 g.

An H-E-B worker find a pallet of 20 ounce red sodas, but the labels are missing so he is not sure if it is Big Red or Wild Red. In order to not waste the pallet of soda, he grabs a 20 ounce red soda at random and decides to test the amount of sugar in the drink. He sets up the following hypotheses:

H₀: The 20 ounce soda is Big Red versus H_a: The 20 ounce soda is Wild Red

He will use the following rule:
If the sugar content of the 20 ounce red soda is 65 g or more, he will decide that the soda is Wild Red (H_a).
But if the sugar content of the 20 ounce red soda is less than 65 g, he will decide that the soda is Big Red (H₀).

For this situation, find the value of β.--------Please show work!!

• 0.0228

• 0.0344

• 0.0409

• 0.05

• 0.0951

• 0.10

• 0.9000

• 0.9049

• 0.9500

• 0.9591

• 0.9656

• 0.9772

Answer 1