Question

(3.3.8) A data set lists weights​ (lb) of plastic discarded by households. The highest weight is 5.64 ​lb, the mean of all of the weights is x=2.112 ​lb, and the standard deviation of the weights is s=1.111 lb.
a. What is the difference between the weight of 5.64 lb and the mean of the​ weights?
b. How many standard deviations is that​ [the difference found in part​ (a)]?
c. Convert the weight of 5.64 lb to a z score.
d. If we consider weights that convert to z scores between -2 and 2 to be neither significantly low nor significantly​ high, is the weight of 5.64 lb​ significant?

Answer 1

$\bar{x}=2.112\ lb, s=1.111\ lb$

a. $x=5.64\ lb$

$$x-\bar{x}=5.64\ lb-2.112\ lb=3.528\ lb$$

b.

$$\dfrac{x-\bar{x}}{s}=\dfrac{3.528\ lb}{1.111\ lb}\approx3.1755$$

The difference is approximately 3.1733  standard deviations.

c.

$$z=\dfrac{x-\bar{x}}{s}\approx31755$$

d.Since $3.1755>2,$ then the weight of 5.64 lb​ is significant.