Question

A data set lists weights​ (lb) of plastic discarded by households. The highest weight is

Answer 1

Answer:

(a) The difference between the highest weight and mean weight is 3.051 lb.

(b) The number of standard deviations is 2.77.

(c) The z-score of 5.26 is 2.77.

(d) The weight of 5.26 lb is significantly​ high.

Step-by-step explanation:

The random variable X is defined as the weights​ (lb) of plastic discarded by households.

The highest weight is, $X_{max.}=5.26\ lb$

The mean weight is, $\bar x=2.209\ lb$.

The standard deviation of the weight is, $s=1.101\ lb$.

(a)

Compute the difference between the highest weight and mean weight as follows:

$X_{max.}-\bar x=5.26-2.209=3.051$

Thus, the difference between the highest weight and mean weight is 3.051 lb.

(b)

Compute the number of standard deviations the mean is from the maximum  value as follows:

$Number\ of\ standard deviation=\frac{X_{max.}-\bar x}{s}=\frac{3.051}{1.0101}=2.77$

Thus, the number of standard deviations is 2.77.

(c)

The formula of z-score is:

$z=\frac{X-\bar x}{s}$

Compute the z-score for X = 5.26 as follows:

$z=\frac{X-\bar x}{s}=\frac{5.26-2.209}{1.101}=2.77$

Thus, the z-score of 5.26 is 2.77.

(d)

The z-scores between -2 and 2 are considered as neither significantly low nor significantly​ high.

The z-score for X = 5.26  is 2.77.

The value of z > 2.

Thus, the weight of 5.26 lb is significantly​ high.