Question

The average amount of a beverage in randomly selected 16-ounce beverage can is 15.9 ounces with a standard deviation of 0.5 ounces. If a random sample of forty-nine 16-ounce beverage cans is selected, what is the probability that mean of this sample is less than 16.1 ounces of beverage?  (keep 4 decimal places)

Answer 1

Solution :

mean = = 15.9

standard deviation = = 0.5

n = 49

= = 15.9

= / n = 0.5 / 49 = 0.071

P( > 16.1) = 1 - P( < 16.1)

= 1 - P[( - ) / < (16.1 - 15.9) /0.07 ]

= 1 - P(z < 2.8)

Using z table,    

= 1 - 0.9974

= 0.0026