Question

A box of oatmeal must contain 16 oz. The machine that fills the oatmeal boxes is set so that, on the average, a box contains 16.5 oz. The boxes filled by the machine have weights that can be closely approximated by a normal curve. What fraction of the boxes filled by the machine are underweight if the standard deviation is as follows? 29. 0.5 oz 30. 0.3 oz 31. 0.2 oz 32. 0

Answer 1

Answer:

29. 15.87%

30.  4.75%

31. 0.62%

32. probability cannot be calculated (0%)

Step-by-step explanation:

We have that the formula of the normal distribution is:

z = (x - m) / sd

where x is the value we are going to evaluate, m is the mean and sd is the standard deviation

x = 16 and m = 16.5

when sd = 0.5

z = (16 - 16.5) /0.5

z = -1

Now when looking in the z table, we have that the corresponding value is 0.1587, that is, the probability is 15.87%

when sd = 0.3

z = (16 - 16.5) /0.3

z = -1.67

Now when looking in the z table, we have that the corresponding value is 0.0475, that is, the probability is 4.75%

when sd = 0.2

z = (16 - 16.5) /0.2

z = -2.5

Now when looking in the z table, we have that the corresponding value is 0.0062, that is, the probability is 0.62%

when sd = 0

z = (16 - 16.5) / 0

z = infinity

probability cannot be calculated