Question

Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a normal distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce. for the distribution, approximately what percent of the bags will likely be underweight (that is, less than 16 ounces)?

Answer 1

To solve this we use the z statistic. The formula for z score is:

z = (x – u) / s

where x is the sample value = less than 16, u is the sample mean = 16.1, s is standard dev = 0.1

 

z = (16 – 16.1) / 0.1

z = - 1

 

From the standard distribution tables at z = - 1,

P (z = -1) = 0.1587

 

So about 15.87% is underweight.