Problem 36BSC

Identifying Unusual Values with the Range Rule of Thumb. In Exercises,use the range rule of thumb to determine whether a value is unusual.

Weights of Pepsi Based on Data Set 19, cans of regular Pepsi have weights with a mean of 0.82410 lb and a standard deviation of 0.00570 lb. Is it unusual for a can to contain 0.8133 lb of Pepsi? Explain.

Problem 36BSC

Answer:

Step1 of 3:

We have Based on Data Set 19, cans of regular Pepsi have weights with a mean of 0.82410 lb and a standard deviation of 0.00570 lb.

Step2 of 3:

We need to determine whether a value is unusual by using thumb rule.Is it unusual for a can to contain 0.8133 lb of Pepsi? Explain.

Step3 of 3:

According to the range rule of thumb, most values should lie within 2 standard deviations of the mean.We can therefore identify “unusual” values by determining if they lie outside these limits:

Maximum usual value = μ + 2σ

Minimum usual value = μ – 2σ

We have

Now,

1).Maximum usual value = μ + 2σ

= 0.8241 + 2(0.00570)

= 0.8241 + 0.0114

= 0.8355.

2).Minimum usual value = μ – 2σ

= 0.8241 - 2(0.00570)

= 0.8241 - 0.0114

= 0.8127.

Since 0.8355 < 0.8133 < 0.8127, we know that 0.8133 lb of pepsi is not unusual.